Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 5 - Linear Functions - 5-5 Standard Form - Practice and Problem-Solving Exercises - Page 327: 61


$4x - y = -2$

Work Step by Step

The equation given is in standard form, so we want to change it to slope-intercept form to be able to see what the slope is. The slope-intercept form is given by the formula: $y = mx + b$ To isolate the $y$ term, let us subtract the $x$ term from each side of the equation: $-y = -4x + 5$ Divide all terms on each side by $-1$ to isolate $y$: $y = 4x - 5$ This line has a slope of $4$; therefore, the equation of the line we want to find also has a slope of $4$. We can get the y-intercept of the equation we are looking for from the second equation we are given. Let us also rewrite this equation in slope-intercept form to find the y-intercept. First, we add the $x$ term to both sides to isolate the $y$ term: $3y = 13x + 6$ Divide both sides by $3$ to isolate $y$: $y = \frac{13}{3}x + 2$ We see that the y-intercept of this graph is $2$; therefore, the y-intercept of the equation of the line we are looking for is also $2$. Now that we have both the slope and y-intercept of the line we are looking for, we can plug in these values into the slope-intercept form: $y = 4x + 2$ We need to rewrite this equation in standard form ($Ax + By = C$). First, let us subtract $4x$ from each side: $-4x + y = 2$ Let's divide all terms by $-1$ so that the $x$ term is not negative: $4x - y = -2$
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