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) Number of calories
Burned

3 15
6 30
9 45
12 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.

To write an equation that represents the relationship between the time Sabir runs (x) and the number of calories he burns (y), we need to look for a pattern in the table.

From the table, we can see that as the time Sabir runs increases by 3 minutes, the number of calories burned increases by 15. This means that there is a constant rate of change of 15 calories per 3 minutes.

To find the equation, we can use the slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.

The slope (m) represents the rate at which the calories burned change per minute. In this case, since the rate is 15 calories per 3 minutes, we can simplify it to 5 calories per minute. So, m = 5.

The y-intercept (b) represents the initial number of calories burned when no time has passed. Looking at the table, when x = 0, y = 0. Therefore, the y-intercept is 0. So, b = 0.

Plugging these values into the slope-intercept form, we get the equation:

y = 5x + 0

Simplifying it further, we have:

y = 5x

Thus, the equation that represents the relationship between the time Sabir runs (x) and the number of calories he burns (y) is y = 5x.