AOn the given graph, the x-axis represents the time in minutes, while the y-axis represents the number of heartbeats.
BOn the given graph, the x-axis represents the time in minutes, while the y-axis represents the number of heartbeats.
CFor each line on the graph, start by writing the ratio of the y-coordinate to the x-coordinate using one point on the line.
ASee solution.
BSee solution.
CActive Heart Rate: 60 heartbeats per minute Hibernating Heart Rate: 12 heartbeats per minute
Practice makes perfect
Let's start by taking a closer look at the given graph.
For each point on the graph, the x-coordinate is the amount of time in minutes and the y-coordinate is the number of heartbeats for an adult brown bear in that amount of time. Therefore, the point ( 2, 120) tells us that the bear's heart beats on average 120 times in 2 minutes. Since the point ( 2, 120) lies on the blue line, it refers to active bears.
Now we want to determine what the ratio of the y-coordinate to the x-coordinate represents for each pair of the given points. Let's start by considering the first pair of points.
(1.5,90) and (2,120)
On the graph, the x-axis represents the time in minutes while the y-axis represents the number of heartbeats. Since the two points lie on the blue line, they refer to active bears. This means that the ratio of the y-coordinate to the x-coordinate represents the average number of heartbeats for an active brown bear. Next, we will consider the second pair of points.
(1.5,18) and (2,24)
Since these two points lie on the red line, they refer to hibernating bears. This means that the ratio of the y-coordinate to the x-coordinate represents the average number of heartbeats for a hibernating brown bear.
We want to find the bear's average heart rate when it is active and when it is hibernating. We will start with the case when a bear is active. To find the active bear's average heart rate, we can use one of the points that lie on the blue line. Let's write the ratio of y-coordinate to the x-coordinate for the point ( 2, 120).
120 heartbeats/2minutes
Recall that a unit rate is a rate that has been reduced to a denominator of 1 unit. In this case, the unit rate is the number of heartbeats per minute for an active bear. Let's find the unit rate! To keep things simple, let's ignore the units for now.
We found the unit rate!
120 heartbeats/2minutes = 60 heartbeats/1minute
As we can see, the active bear's average heart rate is 60 heartbeats per minute. Next, we will calculate the hibernating bear's average heart rate. To do so, we will write a ratio using one of the point that lie on the red line.
( 2, 24) → 24 heartbeats/2minutes
Now we will find the unit rate the same way we did before.
