Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.3 Lines - F.3 Assess Your Understanding - Page 29: 14


a) $m=\dfrac{1}{3}$ b) If $x$ increases by $3$ units, $y$ will increase by $1$ unit.

Work Step by Step

a) The slope of the line that passes throught two points $(x_1, y_1)$ and $(x_2, y_2)$ can be found using the formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$ Thus, the slope of the line passing through the two given points is: $m=\dfrac{2-1}{2-(-1)}=\dfrac{1}{3}$ b) Interpreting the slope, we can say that it means how much $y$ changes when $x$ changes. More formally, for every $3$ units change in $x$, $y$ will change by $1$. That is, if $x$ increases by $3$ units, $y$ will increase by $1$ unit.
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