Plz Help with Derivatives

Question

Let f(8)=4 and f'(8)= -1

Then the equation to the tangent line of the graph y=f(x) at x=8 is

y= _________

Answer 1

The equation of a line in point-slope form is (y - y₁) = m(x - x₁) where m is the slope and a point on the line is (x₁, y₁)

In calculus, when we take the derivative at a point, the value is the slope of the tangent line at that point. So, if f '(8) = -1, then the slope of the tangent line at x = 8 is -1 (m = -1). Since f(8) = 4, a point on the line is (8, 4).

So, plugging those into the point-slope equation, we get (y - 4) = -1(x - 8). If you want to switch this around, you can multiply it out and combine like terms to get y = -x +12

Answer 2

find the line that goes through point (8,4) and its slope is -1.

-1 = (y-4)/(x-8)

Thus, y = -x + 12