As part of a new fitness plan, Sabir runs on a treadmill at the same speed for 15 minutes every morning. The table shows the calories he burns over time.
Time (in minutes) 3 , 6, 9, 12,
Number of calories
Burned 15, 30, 45, 60,
Write an equation to represent the relationship between the time Sabir runs and the number of calories he burns. Use x as the independent variable and y as the dependent variable.
Burns 5 calories/minute.
x = 5y
12
To write an equation that represents the relationship between the time Sabir runs (in minutes) and the number of calories he burns, we can use the given data points.
We can observe that the number of calories burned is directly proportional to the time Sabir runs. More specifically, for every 3 minutes, the number of calories burned increases by 15.
Let's break down the steps to find the equation:
Step 1: Determine the constant rate of change (slope):
To find the constant rate of change, we can calculate the change in calories burned divided by the change in time. Let's take the first two data points:
Change in calories burned = 30 - 15 = 15
Change in time = 6 - 3 = 3
The constant rate of change (slope) is calculated as follows:
slope = change in y / change in x
slope = 15 / 3
slope = 5
Step 2: Determine the y-intercept:
To find the y-intercept, we can pick any point on the line (0, y) where y represents the number of calories burned. Let's use the point (3, 15):
y = mx + b (where m is the slope and b is the y-intercept)
15 = 5 * 3 + b
15 = 15 + b
b = 0
Step 3: Write the equation:
Now we can substitute the slope (m = 5) and y-intercept (b = 0) into the equation:
y = mx + b
y = 5x
Therefore, the equation representing the relationship between the time Sabir runs (x) and the number of calories he burns (y) is:
y = 5x