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

1 Answer
Jul 11, 2015

Answer:

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#.