Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 213: 68

Answer

$x=3$, $y=-2$, see graph

Work Step by Step

Consider the linear equation given $6x-9y-18=0$ Use intercepts to graph the equation as follows: Step 1: Find the $x$ intercept of the graph. Substitute $y=0$ in the equation $6x-9y-18=0$ and find the value of $x$ $\begin{align} & 6x-9\times 0-18=0 \\ & 6x=18 \\ & x=\frac{18}{6} \\ & =3 \end{align}$ So, the $x$ intercept of the line $6x-9y-18=0$ is 3. Hence, the line passes through the point $\left( 3,0 \right)$. Step 2: Find the $y$ intercept. Substitute $x=0$ in the equation $6x-9y-18=0$ and find the value of $y$: $\begin{align} & 6\times 0-9y-18=0 \\ & -9y=18 \\ & y=\frac{18}{\left( -9 \right)} \\ & =-2 \end{align}$ So, the $y$ intercept of the line $6x-9y-18=0$ is $-2$. Hence, the line passes through the point $\left( 0,-2 \right)$. Step 3: Graph the equation in the rectangular coordinate system. Locate the two intercepts $\left( 3,0 \right)$ and $\left( 0,-2 \right)$. Connect them by a straight line. The graph of the given equation $6x-9y-18=0$ is as follows:
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