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Difficulty: MediumSlope of a Line

A commercial printing press operates at a constant rate throughout the day. At 10:15 a.m., a total of 180 posters have been printed since the morning shift began. By 11:45 a.m. on the same morning, a total of 540 posters have been printed. What is the printing rate of the press, in posters per hour?

Answer: 240 posters per hour

Answer

The printing rate of the press is 240 posters per hour.
The slope of a linear relationship represents the constant rate of change. The total number of posters increases by 540−180=360540 - 180 = 360 over an elapsed time of 1.51.5 hours. Dividing the change in posters by the change in time yields 3601.5=240\frac{360}{1.5} = 240 posters per hour.

Step-by-Step Solution

1
Determine the change in the dependent variable (number of posters printed)
540−180=360540 - 180 = 360 posters
Slope represents the change in yy divided by the change in xx, where yy is the total posters printed.
2
Determine the change in the independent variable (time in hours)
From 10:15 a.m. to 11:45 a.m. is 1.5 hours
Time must be expressed in hours to match the requested unit of posters per hour.
3
Compute the slope (rate of change)
3601.5=240\frac{360}{1.5} = 240 posters per hour
Dividing total posters printed by total hours gives the constant rate of change.

Key Concept

Interpretation of Slope as a Constant Rate of Change
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Topics

Slope of a Line

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