Question

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 1

The answer is A, 1/4. Hope this helps!

Answer 2

The constant of variation is
`(1)/(4)`

Step-by-step explanation

Method 1

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

`y=kx`

where
`k` is the constant of variation.

We can trace from the diagram that, the points
`(-4,-1)` and
`(4,1)` 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
`(4,1)` to obtain;

`1=4k`

We solve for
`k` to obtain,

`k=(1)/(4)`

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,
`(0,0)` and
`(1,4)` and use it to determine the slope.

`Slope=(1-0)/(4-0)=(1)/(4)`.

Hence the constant of the direct variation is
`(1)/(4)`.