We are given a graph that shows the number of calories burned by hiking.
We also know that the number y of calories burned after x minutes of kayaking is represented by the given linear function.
y=4.5x
Recall that slope is the ratio of the vertical change to the horizontal change between two points.
m = y_2-y_1/x_2-x_1
Since x always represents the minutes performing each activity and y the calories burned, the slope will tells us the amount of calories burned per minute. We will start by calculating the slope of the given hiking line. Let's substitute the points (0,0) and (5,30) into the slope formula and calculating m.
This means that we burn 6 calories per minute by hiking. To find the slope of the kayaking function, remember that functions written in slope-intercept form follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. The given linear function for kayaking shows that the slope is 4.5, which means that we burn 4.5 calories per minute by kayaking. Therefore, hiking burns more calories per minute.
We want to know the total calories burned if we perform each activity for 45 minutes. To do so, we will start by writing a linear function for the line that represents the number of calories burned after x minutes of hiking.
y= mx+ b
From Part A we know that the slope of the line is m= 6. Now, remember that the y-intercept is the value of y where the line crosses the y-axis. It occurs when x=0. In our case, the line passes through the origin then the y-intercept is equal to 0.
y= 6x+ 0 → y=6x
Now that we have the linear function for each activity, we can substitute x= 45 into each function to get the calories burned per activity. Let's start with hiking!
Finally, we will add the calories burned per activity.
Total Calories Burned= 270 + 202.5 = 472.5
Therefore, we burned 472.5 calories by performing each activity 45 minutes.
