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: 49

Answer

\[m=-\frac{a}{b},\text{falls}\].

Work Step by Step

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