Question

For a given curve, what does "find an equation of the tangent line at the given point" instruct?

Answer 1

To find the equation of the tangent line at a given point on a curve, follow these steps: find the slope of the curve at the given point, use the slope-intercept form of a linear equation to write the equation of the tangent line, substitute the coordinates of the given point into the equation to find the value of the y-intercept.

Step-by-step explanation:

To find the equation of the tangent line at a given point on a curve, you need to follow these steps:

1. Find the slope of the curve at the given point.
2. Use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
3. Substitute the coordinates of the given point into the equation to find the value of b.

By following these steps, you can determine the equation of the tangent line.