Question

What is the slope of the linear function `f` that satisfies: `f(2)=-3` and `f(-2)=5`?

Answer 1

Slope = `-2`

Explanation:

We are told that a linear function `f` satisfies:
`f(2)=-3` and `f(-2)=5`

Hence we have a straight line through the points:
`(2,-3)` and `(-2, 5)`

The equation of a straight line through points `(x_1, y_1)` and `(x_2, y_2)` is:

`(y_2 - y_1) = m(x_2-x_1)` where `m` is the slope of the line.

Hence, in our example: `(5-(-3)) = m(-2-2)`

`-4m=8 -> m=-2`

The equation of a straight line is: `y=mx+c`

Hence, in this case: `-3=(-2)*2 +c`

`-3 =-4+c -> c=1`

The graph of `f` is shown below.
graph{-2x+1 [-10, 10, -5, 5]}