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Chapter 13: Problem 15

Plot the following straight lines. Give the values of the \(y\) -intercept and slope for each of these lines and interpret them. Indicate whether each of the lines gives a positive or a negative relationship between \(x\) and \(y\). a. \(y=100+5 x\) b. \(y=400-4 x\)

Short Answer

Expert verified
For the line \(y=100+5 x\), the slope is 5 and the \(y\)-intercept is 100. It shows a positive relationship between \(x\) and \(y\). For the line \(y=400-4 x\), the slope is -4 and the \(y\)-intercept is 400. It shows a negative relationship between \(x\) and \(y\).

Step by step solution

01

Identify the Slope and Y-intercept for Line (a)

From the equation \(y = 100 + 5x\), the slope, \(m\), is 5 and \(y\)-intercept, \(c\), is 100.
02

Interpret and Define Relationship for Line (a)

Since the slope is positive, it shows a positive relationship between \(x\) and \(y\). As \(x\) increases, \(y\) increases. The \(y\)-intercept being 100 tells us that the line intersects the \(y\)-axis at the point (0, 100).
03

Identify the Slope and Y-intercept for Line (b)

From the equation \(y = 400 - 4x\), the slope, \(m\), is -4 and \(y\)-intercept, \(c\), is 400.
04

Interpret and Define Relationship for Line (b)

The negative slope indicates a negative relationship between \(x\) and \(y\), meaning as \(x\) increases, \(y\) decreases. The \(y\)-intercept being 400 means that the line intersects the \(y\)-axis at the point (0, 400).

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