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

Jul 11, 2015

This is a straight line with slope $7$ described by the function
$f \left(x\right) = 7 x - 4$

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

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

where $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are a couple of points through which the line passes.

For example, putting $\left({x}_{1} , {y}_{1}\right) = \left(- 2 , - 18\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(0 , - 4\right)$ we get:

$m = \frac{- 4 - \left(- 18\right)}{0 - \left(- 2\right)} = \frac{14}{2} = 7$

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

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