ANSWER
The constant of variation is [tex]\frac{1}{4}[/tex]
EXPLANATION
Method 1
The general equation of a direct variation is of the form;
[tex]y=kx[/tex]
where [tex]k[/tex] is the constant of variation.
We can trace from the diagram that, the points [tex](-4,-1)[/tex] and [tex](4,1)[/tex] 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 [tex](4,1)[/tex] to obtain;
[tex]1=4k[/tex]
We solve for [tex]k[/tex] to obtain,
[tex]k=\frac{1}{4}[/tex]
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, [tex](0,0)[/tex] and [tex](1,4)[/tex] and use it to determine the slope.
[tex]Slope=\frac{1-0}{4-0}=\frac{1}{4} [/tex].
Hence the constant of the direct variation is [tex]\frac{1}{4} [/tex].
