Question

1. david runs the music - streaming service absolute audio. since upgrading his app last year, david has steadily gained subscribers.
2. this situation can be modeled as a linear relationship.

(there is a line graph here, with the x - axis labeled months since upgrading the app (ranging from 0 to 10) and the y - axis labeled number of subscribers (ranging from 50 to 500). the line starts at (0, 150) and goes up to (10, around 450 - 500).)

1. what does the slope of the line tell you about the situation?
2. options:

david had 350 subscribers 6 months after upgrading the app.
david gained 100 subscribers every 3 months.
david gained 150 subscribers every 3 months.
david had 150 subscribers when he upgraded the app.

Explanation:

Step1: Recall slope interpretation

Slope in a linear model (subscribers vs. months) represents the rate of change of subscribers per month. The formula for slope is $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is change in subscribers, $\Delta x$ is change in months.

Step2: Analyze each option

• Option 1: "David had 350 subscribers 6 months after upgrading" – This is a point on the line (y - value at x = 6), not slope.
• Option 2: Check rate. From x = 0 (upgrade) to x = 3, y goes from 150 to 250. $\Delta y = 250 - 150 = 100$, $\Delta x = 3 - 0 = 3$. So rate is 100 subscribers per 3 months.
• Option 3: $\Delta y$ from 0 to 3 months is 100 (not 150), so incorrect.
• Option 4: "150 subscribers at upgrade" is the y - intercept (x = 0), not slope.

Answer:

David gained 100 subscribers every 3 months.