Before we write an equation for this relation, let's identify a few points on the graph.
Now let's use a table to identify the difference between x- and y-values.
Each time the value of x increases by 4, the value of y increases by 1. A direct variation equation follows the form y=mx, where m is the constant of variation. This value is equal to the ratio of the change in y over the change in x.
m=Change iny/Change inx=1/4
This suggests that the equation for the given relation is y= 14 x or f(x)= 14 x. Let's test a few values of x to see if this equation works.
x
14x
Expected y
Actual y
-4
-1
-1
1
0
0
0
2
4
1
1
3
The actual value of y in the given relation is always 2 greater than 14x. If we add 2 to one side of our direct variation equation, the equation for the relation becomes y= 14x+2 or f(x)= 14x+2.
