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: 74

Answer

$\text{m=}\frac{-b}{a}$ ; falls

Work Step by Step

The slope of a line can be defined as the ratio of the vertical change to the horizontal change when moving from one fixed point to another along a line. The general notation for the slope of a line is, $\left( m \right)$. $\text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}}$ Let $\left( {{x}_{1}},{{y}_{1}} \right)$ represents point $\left( -a,0 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ represents point $\left( 0,-b \right)$ Then, $\begin{align} & \text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}} \\ & =\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & =\frac{\left( -b \right)-0}{0-\left( -a \right)} \\ & =-\frac{b}{a} \end{align}$ Hence, the slope of the line is $-\frac{b}{a}$ As the slope is negative, therefore the line passing through the provided point is falling.
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