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: 69

Answer

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

Work Step by Step

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