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

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Answer 1 · 2015-07-11T20:39:09

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

For any two of these points, if you calculate the slope between them you will find that it is $7$ $7$ . Slope $m$ $m$ 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 $f(x) = 7x-4$ .