Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 3 - Introduction to Graphing - 3.5 Slope - 3.5 Exercise Set: 86

Answer

Each tick mark on the x-axis represents $0.25$ units.

Work Step by Step

Slope is the rise over run (or rise divided by the run). Having a slope of $-\dfrac{2}{3}$ means that the rise is $-2$ and the run is $3$. The two points have unknown x-coordinates but their y-coordinates are known: $(x_1, 3)$ and $(x_2, 2)$ The rise between the two points is $=2-3=-1$ The run is represented by $x_2-x_1$. Thus, the slope is given by: $=\dfrac{\text{rise}}{\text{run}}=\dfrac{-1}{x_2-x_1}$ The slope is $-\dfrac{2}{3}$. Note that $\dfrac{-1}{1.5}=-\dfrac{1}{1.5}=-\dfrac{2}{3}$. So you can have: $\dfrac{-1}{x_2-x_1}=\dfrac{-1}{1.5}$ This means that $x_2-x_1=1.5$ Note that there are six vertical tick marks from $(x_1, 3)$ to $(x_2, 2)$ These vertical tick marks must represent 1.5 units. Divide $1.5$ units by 6 tick marks to have: $=\dfrac{1.5\text{ units}}{6\text{ tick marks}}=0.25$ units per tick mark.
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