Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Section 2.4 - Linear Functions and Slope - Exercise Set: 66

Answer

slope = $\dfrac{a}{b}$; The line through the two given points rises from left to right.

Work Step by Step

RECALL: (i) The slope, $m$, of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m=\dfrac{y_2-y_1}{x_2-x_1}$ (ii) A line whose slope is positive rises from left to right. (iii) A line whose slope is negative falls from left to right. (iv) A horizontal line has a slope of zero. (v) A vertical line has an undefined slope. Use the formula in (i) above to find the slope of the line that passes through the points $(a-b, c)$ and $(a, a+c)$ to obtain: $m=\dfrac{(a+c) -c }{a-(a-b)} \\m=\dfrac{a+c-c}{a-a+b} \\m=\dfrac{a}{b}$ $\dfrac{a}{b}$ is positive. Thus, the line through the two given points rises from left to right.
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