Find equation of tangent line

The derivative \ ( y^ {\prime} (x)= \) The slope of the tangent line is \ ( m_ {1}= \) The equation of the tangent line is \ ( y= \) The slope of the normal line is \ ( m_ {2}= \) The equation of the normal line is \ ( y= \) The equation of the tangent This problem has been solved! See the answer Show transcribed image text Expert AnswerFINDING EQUATION OF TANGENT LINE WITH DERIVATIVES. The formula given below can be used to find the equation of a tangent line to a curve. Here m is the slope of the tangent line and (x1, y1) is the point on the curve at where the tangent line is drawn. Find the equation of the tangent line at x = 5 to the curve f (x) = √ (2x - 1). Substitute ... The Tangent Line Formula of the curve at any point ‘a’ is given as, y − f ( a) = m ( x − a) Where, f (a) is the value of the curve function at a point ‘ a ‘. m is the value of the derivative of the curve function at a point ‘ a ‘. Solved Examples. Question 1: Find the tangent line of the curve f (x) = 4x 2 – 3 at x 0 = 0 ? With these formulas and definitions in mind you can find the equation of a tangent line. Consider the following problem: Find the equation of the line tangent to f (x)=x2at x =2. Having a graph is helpful when trying to visualize the tangent line. Therefore, consider the following graph of the problem: 8 6 4 2 So it will be one half so far out of the equation of the tangent line, it'll be why -1/16 equals one half Times X -1/2. And so Why -1/16 equals 1/2 X -1 quarter. And why equals one half x. And we're adding 1/16 to a quarter. So a quarter is 4/16. We're adding one. We're going to have a -3/16. And this over here is the equation of the tangent line.Q: Find an equation for the line perpendicular to the tangent line to the curve y = x3 - 4x + 1 at the… A: Click to see the answer Q: Calculate the equation of the tangent line to the curve 2x 3 + xy + 3x + y = 2 at the point (0, 2).14. Find the equation of the line tangent to the graph of g (x) = 4 x 3 2 when x = 1. 15. The line defined by the equation 2 1 x + 3 = − 2 (y − 3) is the line tangent to the graph of a function f (x) when x = a. What is the value of f ′ (a)? Show your work and explain your reasoning. 16.To find the equation of a tangent using implicit differentiation: Differentiate the function implicitly. Evaluate the derivative using the x and y coordinate values to find ‘m’. Substitute the x and y coordinates along with this value of m into (y-y1)=m(x-x1). For example, find the equation of the tangent to at the point (3, 2). Step 1. Tangent line calculator. f (x) =. x 0 =. Calculate. The tool that we put at your disposal here allows you to find the equation of the tangent line to a curve in a simple and intuitive way. To achieve this, you just need to enter the function of the curve and the value of x0 of the point where you want to find the tangent line. notion icons Then we can use these values centre and radius to find the equation of the circle. Q4. How is a tangent line related to the radius of the circle? Ans: When a radius of a circle is drawn from the centre to the point of tangency, it is perpendicular to the tangent line at that point. Q5. What is the definition of tangent lines to circles? Question. Find an equation of the tangent line to the graph of at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. f (x)=5 x^ {2}+6 x-1 f (x) = 5x2 +6x− 1; (-1, -2)When using the slope of tangent line calculator , the slope-intercept formula for a line is found by the formula below: y = mx + b. Where. m stands for the slope of the line . b is the y-intercept. For instance, when you enter the curve, y= 4x^2-4x+1 at x=1, in our tangent line finder, the result will be as follows: y= 4x2-4x+1 at x=1.When y = f (x) is the given curve, the slope of the tangent is, so by point-slope formula, the tangent line equation at (X, Y) is y - Y = dydx (X). (x - X) Here (x, y) coordinates on the tangent line, and the derivative is calculated at x = X.With these formulas and definitions in mind you can find the equation of a tangent line. Consider the following problem: Find the equation of the line tangent to f (x)=x2at x =2. Having a graph is helpful when trying to visualize the tangent line. Therefore, consider the following graph of the problem: 8 6 4 2Sep 28, 2014 · Substitute that point and the derivative into the slope intercept formula, y = mx +b, to find the y -intercept. Lastly, the equation of the tangent line is found by substituting in the derivative and y -intercept into the slope intercept formula, y = mx + b. Answer link Find the equation of the tangent to the circle x 2 + y 2 = 16 which are (i) perpendicular and (ii) parallel to the line x + y = 8. Solution : Equation of tangent to the circle will be in the form. y = mx + a √(1 + m 2) here "m" stands for slope of the tangent ,.find equation of the tangent line. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…So it will be one half so far out of the equation of the tangent line, it'll be why -1/16 equals one half Times X -1/2. And so Why -1/16 equals 1/2 X -1 quarter. And why equals one half x. And we're adding 1/16 to a quarter. So a quarter is 4/16. We're adding one. We're going to have a -3/16. And this over here is the equation of the tangent line. My math homework is finding an equation of the circle. Given that the center is at (-3,-5) and tangent to the line 12x + 5y =4. I don't know how to solve this since our professor didn't teach this to us.Finding function from the tangent line. I have equation for tangent line: y = x + 1 and the tangent line is through point ( x 0, y 0) whose coordinate is ( 0, 1) therefore from this formula m = 1 = e x 0 = e 0 (the slope of the tangent line) and thus the derivative of the function we are searching for is: e x to have the function we are ... Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Here are the steps to take to find the equation of a tangent line to a curve at a given point: Find the first derivative of f (x). A tangent is a line that intersects a curve at only one point and does not pass through it, such that its slope is equal to the curve's slope at that point.Oct 29, 2013 · 1) Denote by A the point ( 4, − 3), by O the center of the circle, and by P 1, P 2 the two points on the circle in which the corresponding tangent line intersects the circle. Then both the triangles A O P 1 and A O P 2 are right, with hypotenuse A O. 2) The length of A O is ( − 2 − 4) 2 + ( − 7 − ( − 3)) 2 = 36 + 16 = 52. The equation of the tangent line can be found using the formula y - y 1 = m (x - x 1 ), where m is the slope and (x 1, y 1) is the coordinate points of the line. State two tangent properties. The tangent line to a circle is always perpendicular to the radius corresponding to the point of tangency.Equation of Tangent line is: (x– x1) = m(y– y1) (x– ( − 4)) = ( − 1)(y– 2) x + 4 = − y + 2. y ... sofa with power recliner The equation of the tangent line to a curve can be found using the form y = m x + b, where m is the slope of the line and b is the y-intercept. Therefore, if we want to find the equation of the tangent line to a curve at the point ( x 1, y 1), we can follow these steps: Step 1: Find the derivative of the function that represents the curve.Jul 20, 2022 · The equation of a tangent to the circle \ ( {x^2} + {y^2} + 2gx + 2fy + c = 0\) at the point \ (\left ( { {x_1},\, {y_1}} \right)\) is given by, \ (x {x_1} + y {y_1} + g\left ( {x + {x_1}} \right) + f\left ( {y + {y_1}} \right) + c = 0\) Slope Form The equation of the tangent line is y − 2 3 = − 3 3 ( x − 2) For reference, the graph of the curve and the tangent line we found is shown below. Advertisement Normal Lines Suppose we have a a tangent line to a function. The function and the tangent line intersect at the point of tangency. Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step ... System of Inequalities Polynomials Rationales Complex Numbers. malvern prep football schedule. serial number lookup for furniture. who am i and who does god want me to become ...Jul 20, 2022 · The equation of a tangent to the circle \ ( {x^2} + {y^2} + 2gx + 2fy + c = 0\) at the point \ (\left ( { {x_1},\, {y_1}} \right)\) is given by, \ (x {x_1} + y {y_1} + g\left ( {x + {x_1}} \right) + f\left ( {y + {y_1}} \right) + c = 0\) Slope Form Finding equation of tangent line at a point [duplicate] Ask Question Asked 8 years, 7 months ago. Modified 5 years, 3 months ago. Viewed 12k times Steps to Use Tangent Line Calculator . Read The procedure to use the online Tangent Line Calculator is as follows below: ☛ Step 1: Enter the Value in the respective input field. ☛ Step 1: Click the "Calculate" Button to get the optimal solution. ☛ Step 1: Finally, Output will be displayed in the new window.Follow the steps given below to find the equation of a parallel line. An online tangent line equation calculator gives the slope and the equation of a tangent line by following these steps.. Calculate the Straight Line Graph. If you know two points, and want to know the "y=mx+b" formula (see Equation of a Straight Line), here is the tool for ... grayson funeral home Substitute the given x-value into the function to find the y-value or point. Calculate the first derivative of f (x). Plug the ordered pair into the derivative to find the slope at that point. Substitute both the point and the slope from steps 1 and 3 into point-slope form to find the equation for the tangent line.Nov 13, 2016 · The gradient of the tangent at any particular point is given by the derivative. f (x) = x3 ∴ f '(x) = 3x2 At (2,8),x = 2 ⇒ f '(2) = (3)22 = 12 So the tangent passes through (2,8) and has gradient m = 12 So, Using y − y1 = m(x −x1), the tangent equation is y − 8 = 12(x −2) ∴ y −8 = 12x −24 ∴ y = 12x −16 Answer link Jim H Nov 13, 2016 Steps to Find the Tangent Line Equation. To find the tangent line equation of a curve y = f(x) drawn at a point (x 0, y 0) (or at x = x 0): Step - 1: If the y-coordinate of the point is NOT given, i.e., if the question says the tangent is drawn at x = x 0, then find the y-coordinate by substituting it in the function y = f(x).Find equations of the tangent line to this curve at the point (2,3,17 v = flow(x,y,z) evaluates the speed profile at the points x, y, and z (The formal, rigorous definition is a bit abstract and probably not relevant 1 Determine the equation of a plane tangent to a given surface at a point Secant Slope Calculator Geogebra Secant Slope. Free ...Find the first derivative and evaluate at x = 4π x = 4 π and y = 0 y = 0 to find the slope of the tangent line. Tap for more steps... 1 1 Plug the slope and point values into the point - slope formula and solve for y y. Tap for more steps... y = x− 4π y = x - 4 πTo find the equation of a tangent using implicit differentiation: Differentiate the function implicitly. Evaluate the derivative using the x and y coordinate values to find ‘m’. Substitute the x and y coordinates along with this value of m into (y-y1)=m(x-x1). For example, find the equation of the tangent to at the point (3, 2). Step 1. Find the equation of the tangent to at the point . Step 1. Differentiate the function and . Step 2. Find f' (a) and f (a) 'a' is the x-coordinate of the point at which the tangent meets the curve. In this example, . is found by substituting into . and so, . is found by substituting into . and so, . Step 3.N(t) = T ′ (t) / | | T ′ (t) | |. This equation is used by the unit tangent vector calculator to find the norm (length) of the vector. If it is compared with the tangent vector equation , then it is regarded as a function with vector value. The principle unit normal vector is. schedulecity Oct 05, 2021 · The tangent line equation can be written as y = f (a) + m (x - a). In this case, the point (a, f (a)) is the point of tangency and the slope is found by taking the limit of (f (x) - f (a))/ (x - a)... Finding The Tangent Line Equation With Derivatives - Calculus Problems 1,014,684 views Feb 20, 2016 This calculus video tutorial shows you how to find the equation of a tangent line with...Apr 03, 2018 · To form the equation we have to base it from the original equation y = mx + c we know that m=3 from dy dx = 3 y = 3x + c use the coordinates given fro x and y values to find c (1,2) x=1 , y=2 (2) = 3(1) + c c = − 1 Then we put c back into the general form to get the final tangent equation y = 3x − 1 Answer link Tangent line calculator. f (x) =. x 0 =. Calculate. The tool that we put at your disposal here allows you to find the equation of the tangent line to a curve in a simple and intuitive way. To achieve this, you just need to enter the function of the curve and the value of x0 of the point where you want to find the tangent line.Q: Consider the following. y = x6/5, (1, 1) Find an equation of the tangent line. y = Find an equation… A: Click to see the answer Q: Find an equation of the curve that at each point (x, y) on the curve the normal is 3x - 1 and the…The tangent line equation we found is y = -3x - 19 in slope-intercept form, meaning -3 is the slope and -19 is the y-intercept. Both of these attributes match the initial predictions. 6 Try a more difficult problem. Here's a run-through of the whole process again. This time, the goal is to find the line tangent to at x = 2:Finding equation of tangent line at a point [duplicate] Ask Question Asked 8 years, 7 months ago. Modified 5 years, 3 months ago. Viewed 12k times The following diagram is an example of two tangent circles . Example 1. Find the length of the tangent in the circle shown below. Solution. The above diagram has one tangent and one secant. Given us the following lengths: PQ = 10 cm and QR =.When using slope of tangent line calculator, the slope intercepts formula for a line is: x = my + b. Where "m" slope of the line and "b" is the x intercept. So, the results will be: x = 4y2- 4y + 1aty = 1. Result = 4. Therefore, if you input the curve "x= 4y^2 - 4y + 1" into our online calculator, you will get the equation of ....Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... payday 2king size upholstered bed frameCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Finding The Tangent Line Equation With Derivatives - Calculus Problems 1,014,684 views Feb 20, 2016 This calculus video tutorial shows you how to find the equation of a tangent line with...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Find an equation of the tangent line to the curve x = t 3 + 5, y = t 2 + 3 at the point corresponding to t = 1. Here is my work (which is wrong according the the online submittion software) First I need a point ( x, y). So I plug t = 1 in the parametric equations to get x = 6 and y = 4. Next, I need m, the slope. So I follow the formula14. Find the equation of the line tangent to the graph of g (x) = 4 x 3 2 when x = 1. 15. The line defined by the equation 2 1 x + 3 = − 2 (y − 3) is the line tangent to the graph of a function f (x) when x = a. What is the value of f ′ (a)? Show your work and explain your reasoning. 16.Tangent line calculator. f (x) =. x 0 =. Calculate. The tool that we put at your disposal here allows you to find the equation of the tangent line to a curve in a simple and intuitive way. To achieve this, you just need to enter the function of the curve and the value of x0 of the point where you want to find the tangent line.b) Find the equation of the tangent line at the point shown where x=2. c) Find two positive values of x in the portion of the curve shown at which there is a vertical tangent line.". In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz ...Find the first derivative and evaluate at x = −1 x = - 1 and y = −1 y = - 1 to find the slope of the tangent line. Tap for more steps... 3 3 Plug the slope and point values into the point - slope formula and solve for y y. Tap for more steps... y = 3x+ 2 y = 3 x + 2 The Tangent Line Formula of the curve at any point ‘a’ is given as, y − f ( a) = m ( x − a) Where, f (a) is the value of the curve function at a point ‘ a ‘. m is the value of the derivative of the curve function at a point ‘ a ‘. Solved Examples. Question 1: Find the tangent line of the curve f (x) = 4x 2 – 3 at x 0 = 0 ? warrensburg cycle tangent\:of\:f(x)=\frac{1}{x^2},\:(-1,\:1) tangent\:of\:f(x)=x^3+2x,\:\:x=0; tangent\:of\:f(x)=4x^2-4x+1,\:\:x=1; tangent\:of\:y=e^{-x}\cdot \ln(x),\:(1,0) tangent\:of\:f(x)=\sin (3x),\:(\frac{\pi }{6},\:1) tangent\:of\:y=\sqrt{x^2+1},\:(0,\:1) Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... Find equations of the tangent line to this curve at the point (2,3,17 v = flow(x,y,z) evaluates the speed profile at the points x, y, and z (The formal, rigorous definition is a bit abstract and probably not relevant 1 Determine the equation of a plane tangent to a given surface at a point Secant Slope Calculator Geogebra Secant Slope. Free ...Find the equations of the tangent lines to the curve y = x − 1 x + 1 that are parallel to the line x − 2y = 2. There is a bit of algebra and arithmetic for this. Let's focus on the reasoning and the calculus. One A line parallel to x −2y = 2 must have the same slope. The slope of this line is 1 2. So we want the slope of the tangent line to be 1 2Tangent line calculator. f (x) =. x 0 =. Calculate. The tool that we put at your disposal here allows you to find the equation of the tangent line to a curve in a simple and intuitive way. To achieve this, you just need to enter the function of the curve and the value of x0 of the point where you want to find the tangent line.To find the equation of a tangent line, first, find the equation of a secant line and then allow the two points used from the secant line to become arbitrarily close by taking a limit.Mar 31, 2022 · The formula for a tangent line whose slope is m and the point given is (x⁠⁠⁠⁠⁠⁠⁠ 1, y⁠⁠⁠⁠⁠⁠⁠ 1 ) is given by, y – y⁠⁠⁠⁠⁠⁠⁠1 = m × (x – x⁠⁠⁠⁠⁠⁠⁠1 ) or y= mx + c where c is some constant How to Find the Slope of a Tangent Line? Solution: td webbroker login Question. Find an equation of the tangent line to the graph of at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. f (x)=5 x^ {2}+6 x-1 f (x) = 5x2 +6x− 1; (-1, -2)My math homework is finding an equation of the circle. Given that the center is at (-3,-5) and tangent to the line 12x + 5y =4. I don't know how to solve this since our professor didn't teach this to us.Equation of the tangent line : y-y 1 = m(x-x 1) y+11 = -3(x-3) y+11 = -3x+9. 3x+y+11-9 = 0. 3x+y+2 = 0. Equation of the tangent line is 3x+y+2 = 0. Example 3 : Find a point on the curve. y = x 2-2x-3 . at which the tangent is parallel to the x axis. Solution : y = x 2-2x-3. If the tangent line is parallel to x-axis, then slope of the line at ...Steps to Find the Tangent Line Equation. To find the tangent line equation of a curve y = f(x) drawn at a point (x 0, y 0) (or at x = x 0): Step - 1: If the y-coordinate of the point is NOT given, i.e., if the question says the tangent is drawn at x = x 0, then find the y-coordinate by substituting it in the function y = f(x).Process to find the equation for the tangent line to a curve The equation of the tangent line to a curve can be found using the form y = m x + b, where m is the slope of the line and b is the y-intercept. Therefore, if we want to find the equation of the tangent line to a curve at the point ( x 1, y 1), we can follow these steps: project on world bank pdf. Find equations for the tangent line and normal line to the circle at each given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the equation, tangent line, and normal line.Two circles of radius 4 are tangent to the graph of y^2 = 4x at the point (1, 2)..Apr 03, 2018 · To form the equation we have to base it from the original equation y = mx + c we know that m=3 from dy dx = 3 y = 3x + c use the coordinates given fro x and y values to find c (1,2) x=1 , y=2 (2) = 3(1) + c c = − 1 Then we put c back into the general form to get the final tangent equation y = 3x − 1 Answer link find equation of the tangent line. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…Show he is wrong. The gradient of a line is the value obtained from the tangent of the angle of inclination of the line with respect to the x-axis. m = Tanθ. Equation of a Line: The equation of a line is also helpful to find the gradient of a line. The standard form of the equation of a line, having the equation ax + by + c = 0, has a gradient ...Question. Find an equation of the tangent line to the graph of at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. f (x)=5 x^ {2}+6 x-1 f (x) = 5x2 +6x− 1; (-1, -2)Calculus questions and answers. Find an equation of the tangent line to the graph of y = g (x) at x = 5 if g (5) = −6 and g' (5) = 4. (Enter your answer as an equation in terms of y and x.) Question: Find an equation of the tangent line to the graph of y = g (x) at x = 5 if g (5) = −6 and g' (5) = 4. (Enter your answer as an equation in ...Find an equation of the tangent line to the curve x = t 3 + 5, y = t 2 + 3 at the point corresponding to t = 1. Here is my work (which is wrong according the the online submittion software) First I need a point ( x, y). So I plug t = 1 in the parametric equations to get x = 6 and y = 4. Next, I need m, the slope. So I follow the formulaThis calculus video tutorial shows you how to find and write the equation of the horizontal tangent line and normal line and point slope form and slope inter... planted fish tankThe following diagram is an example of two tangent circles . Example 1. Find the length of the tangent in the circle shown below. Solution. The above diagram has one tangent and one secant. Given us the following lengths: PQ = 10 cm and QR =.14. Find the equation of the line tangent to the graph of g (x) = 4 x 3 2 when x = 1. 15. The line defined by the equation 2 1 x + 3 = − 2 (y − 3) is the line tangent to the graph of a function f (x) when x = a. What is the value of f ′ (a)? Show your work and explain your reasoning. 16.The Tangent Line Formula of the curve at any point ‘a’ is given as, y − f ( a) = m ( x − a) Where, f (a) is the value of the curve function at a point ‘ a ‘. m is the value of the derivative of the curve function at a point ‘ a ‘. Solved Examples. Question 1: Find the tangent line of the curve f (x) = 4x 2 – 3 at x 0 = 0 ? The Tangent Line Formula of the curve at any point ‘a’ is given as, y − f ( a) = m ( x − a) Where, f (a) is the value of the curve function at a point ‘ a ‘. m is the value of the derivative of the curve function at a point ‘ a ‘. Solved Examples. Question 1: Find the tangent line of the curve f (x) = 4x 2 – 3 at x 0 = 0 ? b) Find the equation of the tangent line at the point shown where x=2. c) Find two positive values of x in the portion of the curve shown at which there is a vertical tangent line.". In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz ...Find the first derivative and evaluate at x = 4π x = 4 π and y = 0 y = 0 to find the slope of the tangent line. Tap for more steps... 1 1 Plug the slope and point values into the point - slope formula and solve for y y. Tap for more steps... y = x− 4π y = x - 4 π scamp campersApr 03, 2018 · To form the equation we have to base it from the original equation y = mx + c we know that m=3 from dy dx = 3 y = 3x + c use the coordinates given fro x and y values to find c (1,2) x=1 , y=2 (2) = 3(1) + c c = − 1 Then we put c back into the general form to get the final tangent equation y = 3x − 1 Answer link The Tangent Line Formula of the curve at any point ‘a’ is given as, y − f ( a) = m ( x − a) Where, f (a) is the value of the curve function at a point ‘ a ‘. m is the value of the derivative of the curve function at a point ‘ a ‘. Solved Examples. Question 1: Find the tangent line of the curve f (x) = 4x 2 – 3 at x 0 = 0 ? Sketch the tangent line going through the given point Points on the Line Notice that we have a minimum point which was indicated by a positive a value (a = 1) Cook And Serve Pudding Vs Instant Practice 1 - If the focus of a parabola is (4, -2) and the directrix is y=3, find the equation of parabola Find the equation of the line passing through.Sep 02, 2020 · What you need to do now is convert the equation of the tangent line into point-slope form. The conversion would look like this: y – y1 = m(x – x1). In this equation, m represents the slope whereas x1, y1 is a point on your line. Congratulations! You have found the tangent line equation. Confirm the Tangent Line Equation Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ... If a tangent line to the curve y = f (x) makes an angle θ with x-axis in the positive direction, then dy/dx = slope of the tangent = tan = θ. If the slope of the tangent line is zero, then tan θ = 0 and so θ = 0 which means the tangent line is parallel to the x-axis.Oct 05, 2021 · The tangent line equation can be written as y = f (a) + m (x - a). In this case, the point (a, f (a)) is the point of tangency and the slope is found by taking the limit of (f (x) - f (a))/ (x - a)... The equation of the tangent line to a curve can be found using the form y = m x + b, where m is the slope of the line and b is the y-intercept. Therefore, if we want to find the equation of the tangent line to a curve at the point ( x 1, y 1), we can follow these steps: Step 1: Find the derivative of the function that represents the curve.Here are the steps to take to find the equation of a tangent line to a curve at a given point: Find the first derivative of f (x). A tangent is a line that intersects a curve at only one point and does not pass through it, such that its slope is equal to the curve's slope at that point. virtual railfan xa