College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding: 14

Answer

$m=-\dfrac{1}{2}$ The slope is negative, so the line slants downward from left to right. For every 1 unit increase in the value of $x$, the value of $y$ decreases by $\frac{1}{2}$ unit.

Work Step by Step

RECALL: (1) The slope $m$ of a line can be found using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. (2) The slope can also be described as the $\dfrac{\text{rise}}{\text{run}}$, which can be interpreted as the average increase in $y$ for every unit increase in $x$. (3) A line with a positive slope slants upward from left to right while a line with a negative slants downward from left to right. Using the two given points on the line, solving for $m$ gives: $m=\dfrac{1-0}{-2-0}=\dfrac{1}{-2}=-\dfrac{1}{2}$ The slope is negative, so the line slants downward from left to right. For every 1 unit increase in the value of $x$, the value of $y$ decreases by $\frac{1}{2}$ unit.
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