Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality. Explain your reasoning.

Accepted Solution

Answer:Do not vary directly.Step-by-step explanation:A proportional relation between two variables x and y can be expressed as:y = kxwhere, k is the constant of proportionality.The above equation can be rewritten as:[tex]k=\frac{y}{x}[/tex]This equation should hold true for all the values of x and y that are applicable in the given scenario. This means, if x and y vary directly, the ratio of y to x must be a constant for all the values of y and x.From the given graph, we can see the following points:(0.3, 200) , (0.9, 400), (1.5, 600)For the first point (0.3, 200):[tex]k=\frac{200}{0.3}=666.67[/tex]For the second point (0.9, 400):[tex]k=\frac{400}{0.9}=444.44[/tex]For the third point (1.5, 600):[tex]k=\frac{600}{1.5}=400[/tex]From here we can see that the ratio of y to x is not a constant. This means, the two quantities shown in the graph do not vary directly. There is only a linear relationship between the lines, not a proportional relationship