Question

Does the following set of data represent an inverse or direct variation?

x -1 0 1 2 3

y 2 0 -2 -4 -6



Direct Variation

Inverse Variation

Answer 1

Direct variation

Explanation:

In direct variation, the output is always found by multiplying the input by a certain number, called the constant of variation.

Formula for direct variation: y = kx

Here, when x = -1, y is 2. Subbing these values into y = kx, we get:

2 = k(-1). The const. of var. turns out to be -2.

Now test whether this conclusion applies to the other inputs:

When x = 0, is y = 0, as the table says? Yes.

When x = 1, is y = -2, as the table says? Yes.

Same for inputs 2 and 3; the outputs stem directly from y = -2x.

This set of data represents direct variation.