## Precalculus (6th Edition) Blitzer

Published by Pearson

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

#### Answer

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.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.