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: 70

Answer

x-intercept = -3 y-intercept = 5 Refer to the image below for the graph.
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Work Step by Step

Write the equation in $Ax +By=C$ form. This will make solving for the intercepts a lot easier. The given equation can be rewritten as: $\dfrac{1}{3}x-\dfrac{1}{5}y-2=0 \\\dfrac{1}{3}x-\dfrac{1}{5}y-2+2=0+2 \\\dfrac{1}{3}x-\dfrac{1}{5}y=2 \\15\left(\dfrac{1}{3}x-\dfrac{1}{5}y\right)=-1(15) \\15(\frac{1}{3}x) - 15(\frac{1}{5}y)=-15 \\5x-3y=-15$ To find the $x$ intercept, set $y=0$ then solve for $x$ to obtain: $5x-3y=-15 \\5x-3(0) = -15 \\5x=-15 \\\dfrac{5x}{5}=\dfrac{-15}{5} \\x=-3$ The x-intercept is $-3$. To find the $y$ intercept, set $x=0$ then solve for $y$ to obtain: $5x-3y=-15 \\5(0)-3y = -15 \\-3y=-15 \\\dfrac{-3y}{-3}=\dfrac{-15}{-3} \\y=5$ The y-intercept is $5$. To draw the graph of the equation, plot the x-intercept point $(-3, 0)$ and the y-intercept point $(0, 5)$ and connect them using a straight line. (refer to the attached image in the answer part above)
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