Answer:
Graph 2 has a different constant of proportionality
Step-by-step explanation:
See attachment for graphs
To calculate the constant of proportionality, we simply determine the slope of each graph using
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where x's and y's are corresponding values of x and y
Graph 1:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (0.8,4)[/tex]
Substitute these values in: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4 - 0}{0.8 - 0}[/tex]
[tex]m = \frac{4}{0.8}[/tex]
[tex]m = 5[/tex]
Graph 2:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (10,55)[/tex]
Substitute these values in: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{55 - 0}{10 - 0}[/tex]
[tex]m = \frac{55}{10}[/tex]
[tex]m = 5.5[/tex]
Graph 3:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (4,20)[/tex]
Substitute these values in: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{20 - 0}{4 - 0}[/tex]
[tex]m = \frac{20}{4}[/tex]
[tex]m = 5[/tex]
Graph 4:
[tex](x_1,y_1) = (0,0)[/tex]
[tex](x_2,y_2) = (10,50)[/tex]
Substitute these values in: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{50 - 0}{10 - 0}[/tex]
[tex]m = \frac{50}{10}[/tex]
[tex]m = 5[/tex]
From the calculations above, graph 2 has a different constant of proportionality of 5.5 while others have 5 as their constant of proportionality
