Slope as Unit Rate Quick Check
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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 80 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 20 points per game.
Player A averaged more points than Player B. Player A averaged 20 points per game.
Player B averaged more points than Player A. Player B averaged 75 points per game.
Player B averaged more points than Player A. Player B averaged 75 points per game.
Player B averaged more points than Player A. Player B averaged 45 points per game.
Player A averaged more points than Player B. Player A averaged 20 points per game.
To determine which player averaged more points per game, we need to compare the slopes of the lines on the graphs. The slope represents the rate of change in points per game.
For Player A, the data points are (0, 0), (2, 40), and (4, 80). To find the slope, we use the formula:
slope = (change in y)/(change in x)
slope = (80 - 0)/(4 - 0)
slope = 80/4
slope = 20
So, Player A averaged 20 points per game.
For Player B, the data points are (0, 0), (3, 45), and (5, 75). To find the slope, we use the same formula:
slope = (change in y)/(change in x)
slope = (75 - 0)/(5 - 0)
slope = 75/5
slope = 15
So, Player B averaged 15 points per game.
Since the slope of Player A is higher than the slope of Player B, it means that Player A averaged more points per game. Therefore, the correct answer is:
Player A averaged more points than Player B. Player A averaged 20 points per game.