College Algebra (10th Edition)

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

Chapter 2 - Review Exercises: 25

Answer

x-intercept = 4 y-intercept = 6
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Work Step by Step

RECALL: (1) The y-intercept can be found by letting $x=0$ and then solving for $y$. (2) The x-intercept can be found by letting $y=0$ and then solving for $x$. Solve for the x-intercept by letting $y=0$ and then solving for $x$: $\frac{1}{2}x+\frac{1}{3}y=2 \\\frac{1}{2}x-\frac{1}{3}(0) = 2 \\\frac{1}{2}x-0=2 \\\frac{1}{2}x=2 \\x=2(2) \\x=4$ Solve for the y-intercept by letting $x=0$ and then solving for $y$: $\frac{1}{2}x+\frac{1}{3}y=2 \\ \frac{1}{2}(0)+\frac{1}{3}y=2 \\0+\frac{1}{3}y=2 \\\frac{1}{3}y=2 \\y=2(3) \\y=6$ Thus, the given equation has: x-intercept = 4 y-intercept = 6 Plot the intercept points $(0, 6)$ and $(4, 0)$. Then, connect them using a line to complete the graph. (refer to the attached image in the answer part above for the graph)
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