Answer:
[tex]y=-10x+89[/tex]
Step-by-step explanation:
Remember that the derivative tells us the slope of the tangent line at a given point.
So, we want to find the equation of the tangent line to f(x) at x=8.
We are given that f'(8) is -10.
In other words, the slope of the tangent line to f(x) at x=8 is -10.
We also know that f(8)=9. In other words, we have the point (8,9).
So, we can use the point-slope form to figure out the equation:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute -10 for m and let (8,9) be (x₁, y₁). So:
[tex]y-9=-10(x-8)[/tex]
Distribute the -10:
[tex]y-9=-10x+80[/tex]
Add 9 to both sides:
[tex]y=-10x+89[/tex]
And we're done!
