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: 13

Answer

$m=\dfrac{1−0}{2−0}=\dfrac{1}{2}$ The line slants upward from left to right. For every 2 units increase in the value of x, the value of y increases by 1 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 $\dfrac{rise}{run}$, 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 slope slants downward from left to right. Using the two given points on the line, solving for m gives: $m=\dfrac{1−0}{2−0}=\dfrac{1}{2}$ The slope is positive, so the line slants upward from left to right. For every 2 units increase in the value of x, the value of y increases by 1 unit.
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