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 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.
Player B averaged more points than Player A. Player B averaged 75 points per game.
Player A averaged more points than Player B. Player A averaged 80 points per game.
To determine which player averaged more points per game, we need to compare the slopes of their respective lines on the graphs.
Looking at the graph for Player A, we can see that the line connecting the data points increases by 40 points for every 2 games. This means that the slope of the line for Player A is 40/2 = 20.
Looking at the graph for Player B, we can see that the line connecting the data points increases by 45 points for every 3 games. This means that the slope of the line for Player B is 45/3 = 15.
Since the slope of Player A's line is higher than the slope of Player B's line, it means that Player A averaged more points per game.
Therefore, the correct response is:
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 representing their data points on the graphs.
Let's start with Player A's graph. The data points provided are (0, 0), (2, 40), and (4, 80). We can calculate the slope of the line connecting these points using the formula:
slope = (change in y) / (change in x)
For the first two data points, the change in x is 2 - 0 = 2, and the change in y is 40 - 0 = 40. Therefore, the slope for the first line segment is 40 / 2 = 20.
For the last two data points, the change in x is 4 - 2 = 2, and the change in y is 80 - 40 = 40. Therefore, the slope for the second line segment is 40 / 2 = 20.
Since both line segments have the same slope, we can conclude that the average points per game for Player A is 20.
Now let's move on to Player B's graph. The data points provided are (0, 0), (3, 45), and (5, 75). We can calculate the slope of the line connecting these points using the same formula as before.
For the first two data points, the change in x is 3 - 0 = 3, and the change in y is 45 - 0 = 45. Therefore, the slope for the first line segment is 45 / 3 = 15.
For the last two data points, the change in x is 5 - 3 = 2, and the change in y is 75 - 45 = 30. Therefore, the slope for the second line segment is 30 / 2 = 15.
Again, both line segments have the same slope, so we can conclude that the average points per game for Player B is 15.
Comparing the averages, we find that Player A averaged more points per game than Player B. Therefore, the correct response is:
Player A averaged more points than Player B. Player A averaged 20 points per game.