y = 4x
y = 4.2x
In a linear function of the form [tex]y=mx+b[/tex], [tex]m[/tex] represents the rate.
Since we know that printer A has greater rate than Pinter B, we should find the rate of printer A first. To do it, we will use the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where
[tex]m[/tex] is the slope/rate of the line
[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line
[tex](x_{2},y_{2})[/tex] are the coordinates of the second point
From the table we can get the points (1, 4.25) and (3, 12.75), so [tex]x_{1}=1[/tex], [tex]y_{1}=4.25[/tex], [tex]x_{2}=3[/tex], and [tex]y_{2}=12.75[/tex]. Let's replace those values in our formula to find [tex]m[/tex]:
[tex]m=\frac{12.75-4.25}{3-1}[/tex]
[tex]m=\frac{8.5}{2}[/tex]
[tex]m=4.25[/tex]
Now we can compare the rate of Printer A with the possible rates form Printer B. Since the rate of Printer A is bigger than the one of printer B, the rate of Printer B must be less than 4.25. The only options that satisfy that condition are 4 and 4.2, so the possible equations from printer B are y = 4x and y = 4.2x.
