Graphs of Proportional Relationships Quick Check
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Question
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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?
To find the average number of heartbeats per second, we need to divide the total number of heartbeats by the total time in seconds.
First, we can calculate the total number of heartbeats. The graph shows a line representing resting heart rate, which is a horizontal line at a constant value. Since the y-axis represents heartbeats, the constant value of the line represents the resting heart rate in beats per minute (bpm).
To calculate the total number of heartbeats, we need to multiply the resting heart rate (in bpm) by the total time in minutes. The total time in minutes can be calculated by dividing the total time in seconds by 60 (since there are 60 seconds in a minute).
Let's assume the resting heart rate is given as 60 bpm and the total time in seconds is 60 seconds.
Total time in minutes = 60 seconds / 60 = 1 minute
Total number of heartbeats = Resting heart rate (in bpm) x Total time in minutes
= 60 bpm x 1 minute
= 60 heartbeats
Now, we need to convert the total number of heartbeats into heartbeats per second by dividing it by the total time in seconds.
Average number of heartbeats per second = Total number of heartbeats / Total time in seconds
= 60 heartbeats / 60 seconds
= 1 heartbeat per second
So, the average number of heartbeats per second is 1.
To determine the average number of heartbeats per second, we need to find the slope of the line representing the resting heart rate on the graph.
The slope of a line can be found using the formula: slope = (change in y-axis)/(change in x-axis).
In this case, the change in y-axis represents the change in the number of heartbeats, and the change in x-axis represents the change in time.
Looking at the graph, we can see that the line representing the resting heart rate is a straight line passing through the origin (0,0) and another coordinate point (12, 18).
To find the change in y-axis, we subtract the starting value of y (0) from the ending value of y (18). So, the change in y-axis is 18 - 0 = 18.
Similarly, to find the change in x-axis, we subtract the starting value of x (0) from the ending value of x (12). Therefore, the change in x-axis is 12 - 0 = 12.
Now, we can calculate the slope:
slope = (change in y-axis)/(change in x-axis) = 18/12 = 1.5
Therefore, the average number of heartbeats per second is 1.5.
Note: This assumes a linear relationship between time and heartbeats, and it is specific to the line representing the resting heart rate on the given graph.
To find the average number of heartbeats per second, we need to determine the change in heartbeats and time.
Looking at the graph, we can see that the resting heart rate line starts at 0 heartbeats at 0 seconds and ends at 12 heartbeats at 12 seconds. The change in heartbeats is 12.
Similarly, the change in time is also 12 seconds.
To find the average number of heartbeats per second, we divide the change in heartbeats by the change in time:
Average number of heartbeats per second = Change in heartbeats / Change in time
= 12 heartbeats / 12 seconds
= 1 heartbeats per second
Therefore, the average number of heartbeats per second is 1.