The equation of the line on the graph below is a direct variation equation. what is the constant of the variation?
a. 1/4
b. 1/2
c. 3/4
d. 1

ANSWER

The constant of variation is

EXPLANATION

Method 1

The general equation of a direct variation is of the form;

where is the constant of variation.

We can trace from the diagram that, the points   and lie on the graph of the direct variation.

This means that any of the above points should satisfy the equation of the direct variation when substituted.

Let us substitute to obtain;

We solve for to obtain,

Method 2

The constant of the direct variation is the slope of the straight line.

So we can choose any two points on the line, say, and and use it to determine the slope.

.

Hence the constant of the direct variation is .