College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.3 - Lines - 2.3 Assess Your Understanding: 63

Answer

$\color{blue}{y=2x}$

Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is: $y=mx+b$ where $m$ = slope and $b$ = y-intercept (2) Parallel lines have the same (equal) slopes. (3) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write the given line in slope-intercept form to obtain: $2x-y=-2 \\2x+2=y \\y=2x+2$ This line has a slope of $2$. Since the line we are looking for is parallel to the line above, then its slope is also $2$. Thus, the tentative equation of the line is: $y=2x+b$ The line contains the point $(0, 0)$. This means that the y-intercept of the line is $0$. Therefore, the equation of the line is: $y=2x+0 \\\color{blue}{y=2x}$
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