Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 3 - Introduction to Graphing - 3.2 Graphing Linear Equations - 3.2 Exercise Set - Page 170: 17


Both ordered pairs satisfy the given equation (refer to the step-by-step part below). $(0, 7)$ is also a solution of the equation.

Work Step by Step

An ordered pair (or point) is a solution to a given linear equation if its x and y values satisfy the equation. Substitute the x and y values of each ordered pair into the given equation. For $(2, 1)$: $y+3x=7 \\1+3(2)=7 \\1+6=7 \\7=7$ For $(4, -5)$: $y+3x=7 \\-5+3(4)=7 \\-5+12=7 \\7=7$ Both ordered pairs satisfy the equation, so they are both solutions of the given equation. Plot both points on the same coordinate plane, then connect them using a straight line (refer to the attached graph below). Any other point on the line is a solution of the given equation. Note that the line contains the point $(0, 7)$ so it is also a solution of the equation.
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