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: 61

Answer

$\color{blue}{y=2x+4}$

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). The line is parallel to the line $y=2x$ (whose slope is $2$) This means that the line we are looking for 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 given point to the tentative equation above to obtain: $y=2x+b \\2=2(-1)+b \\2 = -2+b \\2+2=b \\4=b$ Therefore, the equation of the line is: $\color{blue}{y=2x+4}$
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