ANSWER
The constant of variation is \(\frac{1}{4}\)
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,
\(k=\frac{1}{4}\)
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.
\(Slope=\frac{1-0}{4-0}=\frac{1}{4}\).
Hence the constant of the direct variation is \(\frac{1}{4}\).
