College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 62

Answer

Slope = $\dfrac{3}{4}$ y-intercept = $-3$ Refer to the image below for the graph.
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Work Step by Step

RECALL: (1) The slope is equal to $\dfrac{rise}{run}$ and may be used to graph a line when one point on the line is known. (2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope and $b$ = y-intercept. (3) The y-intercept is y-coordinate of the the point on the y-axis where the line passes through. Transform the given equation to slope-intercept form to obtain: $3x-4y=12 \\3x-4y-3x=-3x+12 \\-4y=-3x+12 \\\dfrac{-4y}{-4} = \dfrac{-3x+12}{-4} \\y = \dfrac{3}{4}-3$ This equation has: slope (m) $=\dfrac{3}{4}$ y-intercept (b) $=-3$. To draw the graph of this line using the slope and y-intercept, perform the following steps: (1) Plot the y-intercept point$(0, -3)$. (2) From point $(0, -3)$, use the slope to locate/plot another point. The slope is $\dfrac{3}{4}$, so move up three units (the rise) and move to the right 4 units (the run) to end up at the point $(4, 0)$. (3) Connect the two points using a straight line to complete the graph. (refer to the attached image in the answer part above for the graph)
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