Question

The following table shows several ordered pairs of a function, m(x)

x m(x)
-1 -1.5
1 1.5
2 3
4 6

Graph m(x) on a coordinate plane to determine whether or not the function represents a direct variation. In complete sentences, describe your conclusion and reasoning. Include your graph in your answer.

Answer 1

m(x) = 1.5x . . . . direct variation

Explanation:

You want to know if the function m(x) represents direct variation, given a table of values.

Direct variation

An equation for direct variation is ...

y = kx

where k is a constant that can be found as the ratio of any (x, y) pair:

k = y/x

k = -1.5/-1 = 1.5/1 = 3/2 = 6/4 = 1.5

The ratios are constant, hence m(x) is direct variation with a constant of variation of 1.5.

Graph

The graph of direct variation is a straight line through the origin. The given points lie on such a line.