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

Published by Pearson

Chapter 3 - Introduction to Graphing - 3.3 Graphing and Intercepts - 3.3 Exercise Set - Page 180: 102

Answer

The graphs of the given equation will be parallel to an axis because when you solve for the variable in each equation, you end up getting an equation in the form $x=h$ (a vertical line) or $y=k$ (a horizontal line). A horizontal line is parallel to the x-axis, while a vertical line is parallel to the y-axis.

Work Step by Step

RECALL: (1) The graph of $x=h$ is parallel to the y-axis. (2) The graph of $y=k$ is parallel to the x-axis. Solve the first equation for $x$ to obtain: $Ax+D=C \\Ax=C-D \\\frac{Ax}{A}=\frac{C-D}{A} \\x=\frac{C-D}{A}$ This equation is in the same form as the one in $(1)$ above so its graph is parallel to the y-axis. Solve the second equation for $y$ to obtain: $By+D=C \\By=C-D \\\frac{By}{B}=\frac{C-D}{B} \\y=\frac{C-D}{B}$ This equation is in the same form as the one in $(2)$ above so its graph is parallel to the x-axis. The graphs of the given equations will be parallel to an axis because when you solve for the variable, you get an equation in the form $x=h$ or $y=k$, which is either a vertical line or a horizontal line. A horizontal line is parallel to the x-axis, while a vertical line is parallel to the y-axis.

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