1. Equations of Tangent Lines

2. Objective
To use the derivative to find an equation of a tangent line to a graph at a point.
TS: Explicitly assessing information and drawing conclusions.

3. Equations of Tangent Lines
Find the equation of the tangent line to

4. Equations of Tangent Lines

5. Equations of Tangent Lines
Find the equation of the tangent line to
Slope of f(x) at any x value
Slope of the tangent line at (7, 15)

6. Equations of Tangent Lines
We now have the slope and a point.
We want the equation of the line with
slope of 9 and going through (7,15).

7. Equations of Tangent Lines
Find the equation of the tangent line to

8. Equations of Tangent Lines

9. Equations of Tangent Lines

10. Equations of Tangent Lines
Find the equation of the tangent line to
Slope of f(x) at any x value
Slope of the tangent line at x = 4

11. Equations of Tangent Lines
We now have the slope and the x-coordinate
of a point. We first need to get the y-coor,
then we will have both the slope and the point
for our line.

12. Conclusion
The derivative is a formula used to find the slope of the tangent line to a function.
To find the slope of the tangent line to a function, first, find the derivative and, second, plug the corresponding x-value into the derivative.
To write an equation for the tangent line, use the derivative value (the slope), and the corresponding point on the function.