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Tangent Line Calculator

Calculate the equation of a tangent line to a curve at a given point.

Enter the x-coordinate of the first point

Enter the y-coordinate of the first point

Enter the x-coordinate of the second point

Enter the y-coordinate of the second point

How it works

Calculate the equation of a tangent line to a curve at a given point.


The Formula

y - y1 = m(x - x1)
m = (y2 - y1) / (x2 - x1)

Worked Example

  1. Example: Find the tangent line to the curve y = x^2 at (1, 1)

    Given the curve y = x^2 and the point (1, 1), we can find the slope of the tangent line using the formula m = (y2 - y1) / (x2 - x1).


Tips, Assumptions & Limitations

  • Make sure to enter the correct values for x1, y1, x2, and y2.
FAQ

The tangent line to a curve at a given point is the line that just touches the curve at that point and has the same slope as the curve.

Enter the coordinates of two points on the curve, and the tool will calculate the equation of the tangent line.

Companion article

Tangent Line Calculator: Find the Equation of a Tangent Line

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How this calculator works

The tangent line to a curve at a given point is the line that just touches the curve at that point and has the same slope as the curve.

Explanation

To find the equation of a tangent line, we need to know the slope of the line and a point on the line.

Formula

y - y1 = m(x - x1)
m = (y2 - y1) / (x2 - x1)

Worked example

For example, if we have a curve y = x^2 and we want to find the tangent line at the point (1, 1), we can use the formula to find the slope of the line.

How to use this tool

To use this tool, simply enter the coordinates of two points on the curve, and the tool will calculate the equation of the tangent line.

Frequently asked questions

What is the tangent line to a curve?
The tangent line to a curve at a given point is the line that just touches the curve at that point and has the same slope as the curve.
How do I use this tool?
Enter the coordinates of two points on the curve, and the tool will calculate the equation of the tangent line.

Read the full guide →

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