## College Algebra 7th Edition

Published by Brooks Cole

# Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises - Page 113: 61

#### Answer

slope = $-\dfrac{4}{5}$ y-intercept = $2$ Refer to the image below for the graph.

#### 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: $4x+5y=10 \\4x+5y-4x=-4x+10 \\5y=-4x+10 \\\dfrac{5y}{5} = \dfrac{-4x+10}{5} \\y = -\dfrac{4}{5}+2$ This equation has: slope (m) $=-\dfrac{4}{5}$ y-intercept (b) $=2$. To draw the graph of this line using the slope and y-intercept, perform the following steps: (1) Plot the y-intercept point$(0, 2)$. (2) From point $(0, 2)$, use the slope to locate/plot another point. The slope is $-\dfrac{4}{5}$, so down four units (the rise) and move to the right 5 units (the run) to end up at the point $(5, -2)$. (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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