Table No 1 is proportional because the y-values have a common difference which is 3 and the x-values have a common difference too that is 1. See the graph below.
X-values
3 - 2 = 1
2 - 1 = 1
1 - 0 = 1
Y values
7 - 4 = 3
4 - 1 = 3
1 - -2 = 3
The unit rate of the proportional relationship is the change in y over change in x. Hence, it is 3/1 or 3. The unit rate is 3.
The equation that represents the proportional relationship can be determined using this pattern:
[tex]y=mx+b[/tex]
where m = unit rate and b = the y-intercept or the y-value at x = 0.
Our unit rate is 3 and the y-value at x = 0 is -2. So, the equation for this graph is:
[tex]y=3x-2[/tex]
The equation is y = 3x - 2.
