Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 76


The slope of the line is $m=\frac{a}{b}$.The line rises from left to right.

Work Step by Step

Consider a line passing through the points $\left( a-b,c \right)$ and $\left( a,a+c \right)$. For a line passing through two different points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$, the slope is given by the following equation: $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( a-b,c \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( a,a+c \right)$, and find the slope as below: $\begin{align} & m=\frac{\left( a+c \right)-c}{a-\left( a-b \right)} \\ & =\frac{a+c-c}{a-a+b} \\ & =\frac{a}{b} \end{align}$ Where a and b are positive real numbers. So, the quantity $\frac{a}{b}$ will be positive. Thus, the slope of the given line will be positive. Positive slope indicates that the line will rise from left to right.
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