Question

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

Answer 1

The equation that represents this proportional relationship is y = 12x.

The graph presented illustrates a proportional relationship between the time spent skateboarding and the number of calories burned.

The line begins at the origin (0, 0) and passes through the points (15, 180) and (30, 360), indicating a constant rate of calorie burn per minute.

Since the line passes through the origin and is straight, the equation representing this relationship is of the form y = mx, where 'm' is the slope of the line, 'y' represents the calories burned, and 'x' represents the time in minutes.

To determine the slope 'm', we use the rate at which calories are burned. Between the points (15, 180) and (30, 360), we can calculate the slope by dividing the change in calories by the change in time.

Thus, the slope (m) is 180 calories/15 minutes which simplifies to 12 calories per minute.

Hence, the equation that represents this proportional relationship is y = 12x.