Question

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

Answer 1

Answer: The graph does not show two quantities that vary directly, because the line does not pass through the origin.

Step-by-step explanation:

By definition, you know that Direct variation equations have the following form:

$y=kx$

Where "k" is the constant of proportionality.

The equation means that when "x" increases, "y" increases" and the ratio does not change.

Now, it is very important to remember the following:

 - The graph of a Direct variation equations is a line whose slope is "k".

- The line must passes throug the origin ($Point (0,0)$)

Observe the graph provided.

As you can notice, the line does not pass through the origin; therefore, that graph does not show two quantities that vary directly.