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

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:

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 ()

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.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x