Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter F - Foundations: A Prelude to Functions - Section F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry - F.2 Assess Your Understanding - Page 16: 23

Answer

The $x$-intercept is: $3$. The $y$-intercept is $2$. See the graph below.

Work Step by Step

n order to find the $x$-intercept, we have to plug $y=0$ into the equation, and the $x$-coordinate will give us the intercept itself. $2x+3y=6$ $2x+3(0)=6$ $2x=6$ $x=3$ The same thing should be done for the $y$-intercept, however, here $x=0$ should be plugged into the equation. $2x+3y=6$ $2(0)+3y=6$ $3y=6$ $y=2$ The x-intercept is: $3$. The y-intercept is $2$. Few other points that will help us plot the graph: If $x=-6$ $2(-6)+3y=6$ $3y=18$ $y=6$ The point $(-6,6)$ is on the graph. If $x=-3$ $2(-3)+3y=6$ $3y=12$ $y=4$ The point $(-3,4)$ is on the graph. If $x=6$ $2(6)+3y=6$ $3y=-6$ $y=-2$ The point $(6,-2)$ is on the graph.
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