Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.2 Linear Functions and Their Graphs - Exercise Set 7.2 - Page 430: 50



Work Step by Step

Take \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( -a,0 \right)\]and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( 0,-b \right)\]. Slope of the line is: \[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\] \[\begin{align} & m=\frac{-b-0}{0-\left( -a \right)} \\ & =-\frac{b}{a} \end{align}\] Therefore, the slope of the line is \[-\frac{b}{a}\]. There is a vertical change of \[-b\] units (\[b\]units down) for each horizontal change of \[a\] units. The slope is negative. So, the line falls from left to right.
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