The line can be represented by an equation y=kx, where k is the constant of proportionality. To find k, we can pick any point on the line. For example, let's pick (2,60).
Now, to find the constant of proportionality we need to divide the y-value 60 by the x-value, 2.
k=y/x ⇔ k=60/2=30
We found that the constant of proportionality is 30. Now, let's find the slope of the line. Observing the graph, we can see that the line passes through the points (2,60) and (4,120).
We can see that as the graph travels from left to right, the rise — or change in y — is 60. Similarly, the run — or change in x — is 2.
Slope=Rise/Run ⇔ Slope=60/2=30
The slope is the same as the constant of proportionality — it is equal to 30.
We know that the equation of this line has the following form.
y=mx
Also, we know that m is the slope. In Part A, we found that the slope m is equal to 30. Let's substitute.
y=mx ⇔ y= 30x
We found the equation of the line.
