Slope as Unit Rate Quick Check

Question

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Question
Use the image to answer the question.

An illustration shows two graphs depicting points per game for players A and B. The first graph shows points per game for player A. The horizontal axis shows games ranging from 0 to 5 in increments of 1. The vertical axis shows points ranging from 0 to 85 in increments of 5. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 40 right parenthesis, and left parenthesis 4 comma 80 right parenthesis. A line connects all the data points. The second graph shows points per game for player B. The horizontal axis shows games ranging from 0 to 6 in increments of 1. The vertical axis shows points ranging from 0 to 80 in increments of 5. Three data points are plotted on the graph at left parenthesis 0 comma 0 right parenthesis, left parenthesis 3 comma 45 right parenthesis, and left parenthesis 5 comma 75 right parenthesis. A line connects all the data points.

The average points scored playing basketball for Player A and Player B are graphed in the graphs. Determine which player averaged more points per game.

(1 point)
Responses

Player A averaged more points than Player B. Player A averaged 20 points per game.
Player A averaged more points than Player B. Player A averaged 20 points per game.

Player A averaged more points than Player B. Player A averaged 80 points per game.
Player A averaged more points than Player B. Player A averaged 80 points per game.

Player B averaged more points than Player A. Player B averaged 45 points per game.
Player B averaged more points than Player A. Player B averaged 45 points per game.

Player B averaged more points than Player A. Player B averaged 75 points per game.

Answer 1

To determine which player averaged more points per game, we need to calculate the slope (which represents the average points per game) for both Player A and Player B based on the data points provided in the graphs.

1. Player A:

   • The points at the data points (2, 40) and (4, 80) indicate that for every 2 games, Player A scores 40 points.

   • The average points per game can be calculated using the formula for slope:

     \[ \text{slope} = \frac{\text{change in points}}{\text{change in games}} = \frac{80 - 0}{4 - 0} = \frac{80}{4} = 20 \text{ points per game} \]

2. Player B:

   • The points at the data points (3, 45) and (5, 75) indicate that for every 2 games, Player B scores 30 points more.

   • The average points per game can be calculated similarly:

     \[ \text{slope} = \frac{75 - 0}{5 - 0} = \frac{75}{5} = 15 \text{ points per game} \]

From these calculations:

• Player A averaged 20 points per game.
• Player B averaged 15 points per game.

Thus, Player A averaged more points than Player B. The correct response is:

Player A averaged more points than Player B. Player A averaged 20 points per game.