The graph shows the proportional relationship between time, in minutes, spent skateboarding and the number of calories burned.
Graph with x axis labeled time minutes and y axis labeled calories burned. A line begins at point 0 comma 0 and goes through points 15 comma 180 and 30 comma 360.
Write an equation that represents the relationship.
y = 60x
y equals one twelfth times x
y = 12x
y equals 1 over 60 times x
The equation that represents the relationship is:
y = 12x
To find the equation that represents the relationship between time (x) and calories burned (y) based on the given graph, we can use the slope-intercept form of a linear equation:
y = mx + b
In this case, "m" represents the slope (rate of change) and "b" represents the y-intercept (the value of y when x = 0).
Given that the line passes through the points (0,0), (15,180), and (30,360), we can find the slope (m):
m = (change in y)/(change in x)
= (360-0)/(30-0)
= 360/30
= 12
Now that we have the slope, we can substitute it into the equation along with any given point to find the y-intercept (b). Let's use the point (0,0):
0 = 12(0) + b
0 = b
Therefore, the equation that represents the relationship between time (x) and calories burned (y) is:
y = 12x
To find an equation that represents the relationship between time spent skateboarding (x) and the number of calories burned (y), we need to analyze the graph.
First, let's look at the points provided: (0, 0), (15, 180), and (30, 360).
We notice that as the time increases, the number of calories burned also increases. This indicates a proportional relationship between time and calories burned.
Additionally, we can observe that each time value corresponds to a consistent increase in the number of calories burned. For example, between (0, 0) and (15, 180), the time increases by 15 minutes, and the calories burned increase by 180. The same pattern holds between (15, 180) and (30, 360).
To find the equation, we can calculate the rate of increase by determining the change in y divided by the change in x.
Between (0, 0) and (15, 180):
Change in y = 180 - 0 = 180
Change in x = 15 - 0 = 15
Therefore, the rate of increase is 180/15 = 12.
This means that for every 1 minute increase in time, there is a 12 unit increase in the number of calories burned.
Using the slope-intercept form of a linear equation, which is y = mx + b (where m is the slope and b is the y-intercept), we can substitute the slope (m) as 12 and the y-intercept (b) as 0 (since the line passes through the origin).
Thus, the equation that represents the relationship between time spent skateboarding (x) and the number of calories burned (y) is:
y = 12x