Find the slope of the tangent line to the graph of f at the given point:?

Question

f(x) = -2x + 6 at ( 2, 2)

-6
6
-2
-1/2

Answer 1

The slope of the tangent line to a function f(x) is given by the derivative of f(x) -or- f'(x)

if f(x) = -2x + 6, your derivative is f'(x) = -2

So, the slope of the tangent line to the graph of f is -2 no matter where you are on the curve. This makes perfect sense since f is a line with slope of -2.

Do you remember y = mx + b?

Answer 2

This is a line with a constant slope - 2 which is the same at all the points on the line.

Answer 3

f '(x) = -2 = slope
The slope of f(x) is -2 everywhere. Thus the tangent line has the same slope as the line f(x) and is the tangent line is the line itself.

Answer 4

As this function is a straight line, the slope is clearly -2 at all points!