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: 43

Answer

$\color{blue}{y=2x-3}$

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. Line $L$ is parallel to the line $y=2x$, whose slope is $2$. Since $L$ is parallel to this line, $L$ also has a slope of $2$. Thus, the tentative equation of the line is $y=2x+b$. To find the value of $b$, substitute the x and y values of the point $(3, 3)$ into the tentative equation above to obtain: $y=2x+b \\3=2(3) + b \\3 = 6+b \\3-6=b \\-3=b$ Therefore, the equation of line $L$ is $\color{blue}{y=2x-3}$.
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