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 - 3.3 Graphing and Intercepts - 3.3 Exercise Set - Page 180: 105

Answer

x-intercept: $(40, 0)$ y-intercept: $(0, -\frac{80}{7})$

Work Step by Step

Find the x-intercept by setting $y=0$ then solving for $x$: $2x-7y=80 \\2x-7(0)=80 \\2x=80 \\\frac{2x}{2}=\frac{80}{2} \\x=40$ Thus, the x-intercept is $(40, 0)$. Find the y-intercept by setting $x=0$ then solving for $y$: $2x-7y=80 \\2(0)-7y=80 \\-7y=80 \\\frac{-7y}{-7}=\frac{80}{-7} \\y=-\frac{80}{7}\approx -11.429$ Thus, the y-intercept is $(0, -\frac{80}{7})$. Use a graphing utility to graph the equation and verify the intercepts. (Refer to the attached image below for the graph.)
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