Question

an online music service lets customers download an unlimited number of songs for $0.25 each after paying a monthly membership fee of $5.00. which of the following statements is not true of this situation? a. this situation represents a linear, proportional relationship. b. the constant in the equation for this relationship is 5. c. this situation represents a linear, non - proportional relationship. d. the rate of change for this situation is $\frac{1}{4}$.

Explanation:

Step1: Define the cost - function

Let $x$ be the number of songs downloaded. The total cost $y$ is given by the equation $y = 0.25x+5$.

Step2: Analyze linear - proportional relationship

A linear - proportional relationship has the form $y = kx$ (where $k$ is a non - zero constant and the graph passes through the origin $(0,0)$). The given equation $y=0.25x + 5$ is not of the form $y = kx$ because of the non - zero $y$ - intercept ($b = 5$), so it is a linear non - proportional relationship.

Step3: Identify the constant and rate of change

In the equation $y=mx + b$ (slope - intercept form), $m$ is the rate of change and $b$ is the constant. For $y = 0.25x+5$, the rate of change $m = 0.25=\frac{1}{4}$ and the constant $b = 5$.

Answer:

A. This situation represents a linear, proportional relationship.