Question

How does one find the equation of a tangent line?

Answer 1

To find the equation of a tangent line at a specific point on a curve, you need the coordinates of that point and the slope of the curve at that point. The equation of a tangent line can be found using the point-slope form of a line.

Step-by-step explanation:

The equation of a tangent line can be found using the point-slope form of a line. To find the equation of a tangent line at a specific point on a curve, you need the coordinates of that point and the slope of the curve at that point. Here's how to do it:

1. Find the slope of the curve at the given point. This can be done by taking the derivative of the function representing the curve and evaluating it at the given point.
2. Plug the coordinates of the point and the slope into the point-slope form of a line: y - y1 = m(x - x1)
3. Simplify the equation and rewrite it in the slope-intercept form (y = mx + b) to find the equation of the tangent line.