Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1 - Linear Functions - Chapter Test - Page 123: 4

Answer

Graph of $2x-4y=10$.

Work Step by Step

To graph the given equation, substitute values of $x$ and then solve for $y$. Choosing and substituting $x=1$, the value of $y$ in the given equation is $$\begin{aligned} 2x-4y&=10 \\ 2(1)-4y&=10 \\ 2-4y&=10 \\ -4y&=10-2 \\ -4y&=8 \\ y&=\frac{8}{-4} \\ y&=-2 .\end{aligned} $$Hence, $(1,-2)$ is a point on the line defined by the given equation. Choosing and substituting $x=5$, the value of $y$ in the given equation is $$\begin{aligned} 2x-4y&=10 \\ 2(5)-4y&=10 \\ 10-4y&=10 \\ -4y&=10-10 \\ -4y&=0 \\ y&=\frac{0}{-4} \\ y&=0 .\end{aligned} $$Hence, $(5,0)$ is a point on the line defined by the given equation. Connecting the points $ (1,-2) $ and $ (5,0) $ gives the graph of the given equation.
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