Question

What is the function rule for these ordered pairs (-2, -18) (0, -4) (1, 3) (3, 17)?

Answer 1

This is a straight line with slope `7` described by the function
`f(x) = 7x-4`

Explanation:

For any two of these points, if you calculate the slope between them you will find that it is `7`. Slope `m` is given by the formula

`m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)`

where `(x_1, y_1)` and `(x_2, y_2)` are a couple of points through which the line passes.

For example, putting `(x_1, y_1) = (-2, -18)` and `(x_2, y_2) = (0, -4)` we get:

`m = (-4 - (-18))/(0 - (-2)) = 14/2 = 7`

Since the slope is always `7`, all `4` points are colinear.

We are also given the point `(0, -4)` which allows us to pick out the `-4` term in `f(x) = 7x-4`.