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Chapter 1: Problem 87

The following are the slopes of lines representing annual sales \(y\) in terms of time \(x\) in years. Use the slopes to interpret any change in annual sales for a one-year increase in time. (a) The line has a slope of \(m=135\) (b) The line has a slope of \(m=0\) (c) The line has a slope of \(m=-40\)

Short Answer

Expert verified
(a) For a one year increase in time, sales increase by 135 units. (b) Sales remain constant year over year. (c) For one year increase in time, sales decrease by 40 units.

Step by step solution

01

Explanation of Slopes

In the context of straight line graphs in real-world situations, the slope of a line, denoted by \(m\), represents the rate of change. A positive slope indicates an increasing value, a negative slope indicates a decreasing value, and a slope of zero denotes no change over time.
02

Interpretation of Slope m=135

The slope \(m=135\) implies that for a one year increase in time, annual sales increase by 135 units. This denotes a positive growth in sales year over year.
03

Interpretation of Slope m=0

The slope \(m=0\) represents no change in annual sales irrespective of an increase in time. This means that the annual sales are constant and there is no growth.
04

Interpretation of Slope m=-40

The slope \(m=-40\) suggests that for every one year increase in time, the annual sales drop by 40 units. This indicates a decline in sales year over year.

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