Question

How do you find the slope of the secant lines of `f(x) = -3x + 2` through the points: (-4,(f(-4)) and (1,f(1))?

Answer 1

`-3`

Explanation:

Find the points' `y`-values by evaluating `f(-4)` and `f(1)`:

`f(-4)=-3(-4)+2=12+2=14`

`f(1)=-3(1)+2=-3+2=-1`

The two points on the secant line are `(-4,14)` and `(1,-1)`.

The slope `m` can then be found using the slope equation:

`m=(Deltay)/(Deltax)=(14-(-1))/(-4-1)=15/(-5)=-3`

This should make sense, since `f(x)` is a line. The secant line, which passes through two points on `f(x)`, will have to be the exact same as `f(x)`--there's no other way a line can intercept two points.

Since the secant line is identical to `f(x)`, we can tell that they will have the same slope, and the slope of `f(x)=-3x+2` is `-3`.