Question

the drama students at fremont middle school are selling tickets to their fall play. the scatter plot shows the number of tickets sold each day for the 10 days leading up to the event. on average, for each additional 1 day in ticket sales, there were approximately more tickets sold.

Explanation:

Step1: Identify the slope formula

The slope of a line (which represents the average rate of change here) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Step2: Choose two points on the line

From the graph, the line passes through \((0, 5)\) and \((10, 25)\) (approximate, since at day 10, the line is around 25? Wait, no, looking at the line, when \(x = 0\), \(y=5\); when \(x = 10\), let's check the line. Wait, maybe better to take \((0,5)\) and \((10,25)\)? Wait, no, let's see the line. At day 0, y=5; at day 10, the line is at y=25? Wait, no, the line at day 10: let's calculate the slope. Let's take two points: (0,5) and (10,25). Then \( m=\frac{25 - 5}{10 - 0}=\frac{20}{10}=2 \). Wait, but maybe another pair. Wait, at day 0, y=5; at day 5, y=14? Wait, no, the line at day 5: the line is at y=14? Wait, no, the line passes through (0,5) and let's see, when x=10, the line is at y=25? Wait, maybe the correct two points are (0,5) and (10,25). So the slope is (25 - 5)/(10 - 0)=20/10=2. Wait, but maybe I made a mistake. Wait, the line starts at (0,5) and goes up. Let's check another point: at x=5, the line is at y=14? No, wait, the line's equation: let's use (0,5) as the y-intercept. So y = mx + 5. When x=10, y=25? Then 25 = 10m +5 → 10m=20 → m=2. So the slope is 2. So the average rate of change (tickets per day) is 2.

Answer:

2