Question

What is the constant of proportionality for the proportional relationship shown in the graph?

Answer 1

If you will look at the graph , it is a straight line passing through Origin(0,0) , and if you produce the ray or line from both ends it will lie in first and third Quadrant.

So, equation will be of the form

      y=k x, where k will be any positive real number.

To find equation of line we need two distinct points.

The two points are , (0,0) and (1,2).

Equation of line passing through two points will be

    $\rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\rightarrow \frac{y-0}{x-0}=\frac{2-0}{1-0}\\\\\rightarrow y=2x\\\\\rightarrow \frac{y}{x}=2\\\\\rightarrow \frac{x}{y}=\frac{1}{2}$

⇒Constant of Proportionality will be either 2, or $\frac{1}{2}$.

Answer 2

1 hour for every 2 miles hiked