Graphs of Proportional Relationships Quick Check
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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
3/2
Start Fraction 3 over 2 End Fraction
2/3
Start Fraction 2 over 3 End Fraction
2
2
1/2
To find the constant of proportionality from the graph, we can observe the relationship between the x and y coordinates of the plotted points. In this case, we can see that for every 2 units increase in the x-coordinate, there is a 3 unit increase in the y-coordinate. Therefore, the constant of proportionality is 3/2 or 1.5. Answer: 3/2
To identify the constant of proportionality from the graph, we need to determine the ratio between the change in y-values and the change in x-values.
From the given points, we can see that as x increases by 2 (from 0 to 2), y increases by 3 (from 0 to 3). Similarly, as x increases by another 2 (from 2 to 4), y increases by 3 more (from 3 to 6).
So, the change in y is always 3 times the change in x.
Therefore, the constant of proportionality is 3/2 or "3 halves".
To find the constant of proportionality from the graph, we can look at the ratio of the y-coordinates to the x-coordinates for any two points on the line.
Let's take the points (0, 0) and (2, 3). The ratio of the y-coordinates to the x-coordinates is 3/2.
Similarly, we can take the points (2, 3) and (4, 6). The ratio of the y-coordinates to the x-coordinates is also 3/2.
Since these ratios are equal, we can conclude that the constant of proportionality from the graph is 3/2.
So, the correct answer is "3/2".
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.
What is the average number of heartbeats per second?
(1 point)
Responses
2/3 beat per second
Start Fraction 2 over 3 End Fraction beat per second
1 1/2 beats per second
1 Start Fraction 1 over 2 End Fraction beats per second
3 beats per second
3 beats per second
2 beats per second
To find the average number of heartbeats per second, we need to determine the change in heartbeats divided by the change in time.
From the graph, we can see that the resting heart rate is a straight line. The line passes through the points (0, 0) and (12, 18).
To find the change in heartbeats, we subtract the y-coordinate of the starting point from the y-coordinate of the ending point: 18 - 0 = 18.
To find the change in time, we subtract the x-coordinate of the starting point from the x-coordinate of the ending point: 12 - 0 = 12.
Therefore, the average number of heartbeats per second is 18 divided by 12, which simplifies to 3/2 or 1 1/2 beats per second.
So, the correct answer is "1 1/2 beats per second".