College Algebra (10th Edition)

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

Chapter 5 - Cumulative Review: 5

Answer

The equation of the line is $y=2x-1$ Refer to the image below for the graph.
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Work Step by Step

RECALL: (1) The slope-intercept form of a line is $y=mx+b$ where $m$ = slope of the line and $b$ = y-intercept of the line. (2) Parallel lines have equal or the same slopes. The line is parallel to the line $y=2x+1$, whose slope is $2$. This means that the line also has a slope of $2$. Thus, the tentative equation of the line is: $y=mx+b \\y=2x+b$ The line contains the point $(3, 5)$. This means that the x and y values of this point satisfy the equation of the line. Substitute the x and y values of this point into the line's tentative equation above to obtain: $y=2x+b \\5 = 2(3) + b \\5 = 6+b \\5-6=b \\-1=b$ Thus, the equation of the line is: $y=2x+(-1) \\\color{blue}{y=2x-1}$ To graph the line, perform the following steps: (1) Plot the y-intercept point $(0 ,-1)$. (2) Plot the point on the line $(3, 5)$. (3) Connect the two points using a straight line to complete the graph. (refer to the image in the answer part above for the graph)
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