Question

is the relationship proportional? if so, identify the constant of proportionality and write the equation for the relationship between x and y.

Explanation:

Step1: Check if it's proportional

A relationship is proportional if the graph is a straight - line passing through the origin $(0,0)$. The given graph is a straight - line and passes through the origin, so it is proportional.

Step2: Find the constant of proportionality (k)

The constant of proportionality $k$ in a proportional relationship $y = kx$ can be found by taking any non - zero point $(x,y)$ on the line. Let's take the point $(2,10)$. Then $k=\frac{y}{x}$. Substituting $x = 2$ and $y = 10$ into the formula, we get $k=\frac{10}{2}=5$.

Step3: Write the equation

The equation for a proportional relationship is $y=kx$. Since $k = 5$, the equation is $y = 5x$.

Answer:

The relationship is proportional. The constant of proportionality is $k = 5$ and the equation is $y=5x$.