Slope as Unit Rate Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Ounces and ranges from 0 to 40 in 5 unit increments. The y-axis is labeled Cost in dollars and ranges from from 0.00 to 4.00 in increments of 0.50. The graph is titled Cost per Ounce. A line connects four points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 8 comma 0.80 right parenthesis, left parenthesis 15 comma 1.50 right parenthesis, and left parenthesis 30 comma 3.00 right parenthesis.
The graph displays the cost per ounce of canned peas. Use the graph to determine the unit rate of the proportional relationship.
(1 point)
Responses
Canned peas cost $10 per ounce.
Canned peas cost $10 per ounce.
Canned peas cost $0.10 per ounce.
Canned peas cost $0.10 per ounce.
Canned peas cost $30 per ounce.
Canned peas cost $30 per ounce.
Canned peas cost $3.00 per ounce.
Canned peas cost $3.00 per ounce.
Yes, I am sure. The unit rate is determined by finding the slope of the line connecting the plotted points on the graph. The slope is the change in the y-values divided by the change in the x-values. In this case, the change in y is 3.00 - 0.80 = 2.20 and the change in x is 30 - 8 = 22. Dividing the change in y by the change in x gives us 2.20/22 = 0.10.
Therefore, the unit rate is $0.10 per ounce.
To determine the unit rate of the proportional relationship, we need to find the slope of the line connecting the plotted points on the graph.
The slope of a line is calculated using the formula: slope = (change in y)/(change in x).
Let's calculate the slope using the given coordinates of the plotted points:
Point 1: (0, 0)
Point 2: (8, 0.80)
Point 3: (15, 1.50)
Point 4: (30, 3.00)
Now, calculate the change in y and change in x between each pair of points:
Between Point 1 and Point 2:
Change in y = 0.80 - 0 = 0.80
Change in x = 8 - 0 = 8
Between Point 2 and Point 3:
Change in y = 1.50 - 0.80 = 0.70
Change in x = 15 - 8 = 7
Between Point 3 and Point 4:
Change in y = 3.00 - 1.50 = 1.50
Change in x = 30 - 15 = 15
Now, let's calculate the slope using the formula:
Slope = (Change in y)/(Change in x)
Slope between Point 1 and Point 2: 0.80/8 = 0.10
Slope between Point 2 and Point 3: 0.70/7 = 0.10
Slope between Point 3 and Point 4: 1.50/15 = 0.10
The slope is consistent at 0.10 for all pairs of points.
Therefore, the unit rate of the proportional relationship is $0.10 per ounce.
So, the correct response is:
Canned peas cost $0.10 per ounce.
Are you sure
To determine which player averaged more points per game, we need to compare the y-values (points) on the graphs for Player A and Player B.
Without the graphs or any specific information about the points plotted on the graphs, it is not possible to determine which player averaged more points per game or the specific average points for each player. The correct answer cannot be determined based on the given information.
Slope as Unit Rate Quick Check
3 of 53 of 5 Items
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 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 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 45 points per game.
To determine which player averaged more points per game, we need to compare the slopes (unit rates) of the lines connecting the data points on the graphs for Player A and Player B.
For Player A:
The change in y is 80 - 0 = 80, and the change in x is 4 - 0 = 4.
The slope (unit rate) for Player A is 80/4 = 20.
For Player B:
The change in y is 75 - 0 = 75, and the change in x is 5 - 0 = 5.
The slope (unit rate) for Player B is 75/5 = 15.
Player A had a higher slope (unit rate) of 20, indicating that Player A averaged more points per game compared to Player B.
So, the correct answer is:
Player A averaged more points than Player B. Player A averaged 20 points per game.
Slope as Unit Rate Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis.
Explain why the slope is positive or negative.
(1 point)
Responses
The slope is negative because the line decreases as you move from left to right on the graph.
The slope is negative because the line decreases as you move from left to right on the graph.
The slope is positive because the line increases as you move from left to right on the graph.
The slope is positive because the line increases as you move from left to right on the graph.
The slope is positive because the line decreases as you move from left to right on the graph.
The slope is positive because the line decreases as you move from left to right on the graph.
The slope is negative because the line increases as you move from left to right on the graph.
To determine whether the slope is positive or negative, we can look at the direction in which the line is moving on the graph.
In this case, the line passes through the points (0,0) and (6,6). As we move from left to right on the graph, the line is increasing. This means that the y-values are increasing as the x-values increase.
Since the line is increasing from left to right, the slope is positive.
So, the correct answer is:
The slope is positive because the line increases as you move from left to right on the graph.
What is the slope of the line?
(1 point)
Responses
−1
negative 1
−2
negative 2
1
1
2
To find the unit rate of the proportional relationship, we can use the slope of the line connecting the plotted points. The slope is found by taking the change in y divided by the change in x.
From the graph, we can see that the change in y is 3.00 - 0.80 = 2.20 and the change in x is 30 - 8 = 22.
Therefore, the unit rate is 2.20/22 = 0.10.
So, the correct answer is:
Canned peas cost $0.10 per ounce.