Question

1. book sales a. find the constant rate of change and interpret its meaning. b. determine whether a proportional linear relationship exists between the two quantities shown in the graph. explain your reasoning.

Explanation:

Step1: Calculate the rate of change

The rate of change (slope) for a linear - relationship is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the graph: $(2,1000)$ and $(4,2000)$. Then $m=\frac{2000 - 1000}{4 - 2}=\frac{1000}{2}=500$.

Step2: Interpret the rate of change

The rate of change of 500 means that the number of book - sales increases by 500 per day.

Step3: Check for proportionality

A proportional linear relationship has the form $y = kx$ and passes through the origin $(0,0)$. The graph of book - sales passes through the origin. Also, the rate of change is constant. So, a proportional linear relationship exists.

Answer:

a. The constant rate of change is 500. It means that the number of book - sales increases by 500 per day.
b. Yes, a proportional linear relationship exists. The graph is a straight line passing through the origin and has a constant rate of change.