Question
Use the image to answer the question.
A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
Identify the constant of proportionality from the graph.
(1 point)
Responses
23
Start Fraction 2 over 3 End Fraction
32
Start Fraction 3 over 2 End Fraction
12
Start Fraction 1 over 2 End Fraction
2
2
The constant of proportionality can be found by looking at how the y-coordinate changes as the x-coordinate increases by 1.
From the graph, we can see that as x increases by 1 from 0 to 2, y increases by 3.
Therefore, the constant of proportionality is 3/1, or simplified, 3.
Question
Use the image to answer the question.
A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
Identify the constant of proportionality from the graph.
(1 point)
Responses
2/3
3/2
1/2
2
Apologies for my mistake in the previous response.
To find the constant of proportionality, we need to determine the ratio of the change in the y-coordinate to the change in the x-coordinate.
From the graph, we can see that as x increases by 2 from 0 to 2, y increases by 3.
So, the constant of proportionality is 3/2.
Question
Use the image to answer the question.
A graph shows an x-axis representing time in seconds ranging from 0 to 12 in increments of 2. The y-axis represents heartbeats ranging from 0 to 18 in increments of 3. The graph shows a line representing resting heart rate. The line passes through the following plotted points: left parenthesis 4 comma 6 right parenthesis; left parenthesis 6 comma 9 right parenthesis; left parenthesis 10 comma 15 right parenthesis; and left parenthesis 12 comma 18 right parenthesis.
What is the average number of heartbeats per second?
(1 point)
Responses
3 beats per second
1 1/2 beats per second
2/3 beat per second
2 beats per second
To find the average number of heartbeats per second, we need to calculate the change in the number of heartbeats divided by the change in time.
From the graph, we can see that the change in the number of heartbeats from 4 seconds to 12 seconds is 18 - 6 = 12 beats. The change in time is 12 - 4 = 8 seconds.
Therefore, the average number of heartbeats per second is 12 beats / 8 seconds = 3/2 or 1 1/2 beats per second.
Use the image to answer the question.
A figure shows four graphs labeled A, B, C, and D, each with an x and y axis and 0 at the origin, and each showing a curve. Graph A shows a straight line with a negative slope having x and y intercepts. Graph B shows a straight line with a positive slope having a y intercept above origin. Graph C shows an increasing concave up curve initiating at the origin. Graph D shows a straight line with a unit slope.
Decide which graph shows a proportional relationship.
(1 point)
Responses
D
C
B
A
The graph that shows a proportional relationship is graph A.
In a proportional relationship, the graph would be a straight line passing through the origin (0,0). Graph A fits this description as it is a straight line with a negative slope and has x and y intercepts.
Use the table to answer the question.
Time walking (minutes) 20 30 40 60 80
Calories burned 100 150 200 300 400
The table shows a relationship between the amount of time spent walking and the number of calories burned. Determine if the relationship is proportional.
(1 point)
Responses
The relationship is proportional.
The relationship is non-proportional; the graph does not pass through the origin.
The proportional relationship cannot be determined from the information provided.
The relationship is non-proportional; the graph would be an arc.
To determine if the relationship is proportional, we need to check if the ratio of calories burned to time spent walking is constant.
Let's calculate the ratio for each data point:
For 20 minutes of walking, the ratio is 100 calories / 20 minutes = 5 calories per minute.
For 30 minutes of walking, the ratio is 150 calories / 30 minutes = 5 calories per minute.
For 40 minutes of walking, the ratio is 200 calories / 40 minutes = 5 calories per minute.
For 60 minutes of walking, the ratio is 300 calories / 60 minutes = 5 calories per minute.
For 80 minutes of walking, the ratio is 400 calories / 80 minutes = 5 calories per minute.
The ratio is consistent at 5 calories per minute for each data point. Since the ratio is constant, the relationship is proportional. Therefore, the correct response is:
The relationship is proportional.
To identify the constant of proportionality from the graph, we need to examine the relationship between the x-values and the y-values.
The given points on the graph are (0, 0), (2, 3), and (4, 6).
The constant of proportionality is found by determining the ratio between the change in y-values and the change in x-values.
Let's calculate the ratios for the given points:
For the point (0, 0) to (2, 3), the change in y-values is 3 - 0 = 3, and the change in x-values is 2 - 0 = 2. Therefore, the ratio is 3/2.
Similarly, for the point (2, 3) to (4, 6), the change in y-values is 6 - 3 = 3, and the change in x-values is 4 - 2 = 2. Again, the ratio is 3/2.
Since both ratios are the same, we can conclude that the constant of proportionality is 3/2.
Therefore, the correct answer choice is: Start Fraction 3 over 2 End Fraction.