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

Do not vary directly.

Step-by-step explanation:

A proportional relation between two variables x and y can be expressed as:

y = kx

where, k is the constant of proportionality.

The above equation can be rewritten as:

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):

For the second point (0.9, 400):

For the third point (1.5, 600):

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

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