Graphs of Proportional Relationships Quick Check
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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.
What is the average number of heartbeats per second?
(1 point)
Responses
23 beat per second
Start Fraction 2 over 3 End Fraction beat per second
2 beats per second
2 beats per second
3 beats per second
3 beats per second
112 beats per second
The correct answer is 1/3 beat per second.
To find the average number of heartbeats per second, you need to determine the slope of the line representing the resting heart rate on the graph.
Looking at the graph, we can see that the y-axis represents heartbeats and the x-axis represents time in seconds. The y-axis ranges from 0 to 18 in increments of 3, and the x-axis ranges from 0 to 12 in increments of 2.
Since the graph represents a proportional relationship, the slope of the line will determine the average number of heartbeats per second.
To calculate the slope, we can choose two points on the line. Let's choose (0,0) and (12,18).
The slope, denoted as m, can be calculated using the formula:
m = (change in y) / (change in x)
Using the chosen points, the change in y is 18 - 0 = 18, and the change in x is 12 - 0 = 12.
So, the slope is:
m = 18 / 12 = 1.5
Therefore, the average number of heartbeats per second is 1.5 beats per second.
Therefore, the correct answer is:
1.5 beats per second
To find the average number of heartbeats per second, we need to calculate the slope of the line representing the resting heart rate on the graph.
The slope represents the rate of change, which in this case is the number of heartbeats for each second. We can calculate it by finding the change in y divided by the change in x.
Looking at the graph, we can see that the resting heart rate starts at 0 beats at 0 seconds and ends at 6 beats at 12 seconds.
Change in y = 6 - 0 = 6 beats
Change in x = 12 - 0 = 12 seconds
Now, we divide the change in y by the change in x to find the slope:
slope = change in y / change in x
slope = 6 beats / 12 seconds
Simplifying the fraction, we get:
slope = 1/2 beats per second
Therefore, the average number of heartbeats per second is 1/2 or 0.5 beats per second.
So, the correct answer is:
Start Fraction 2 over 3 End Fraction beat per second