Algebra 1: Common Core (15th Edition)

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

Chapter 5 - Linear Functions - Chapter Review - Page 355: 26

Answer

$y = 5x - 11$

Work Step by Step

We know that two parallel lines have the same slope, so if we are given the equation of a line parallel to the one we are looking for, then we know we already have the slope of our unknown line. The known line is written in slope-intercept form, which is given by the formula: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. So for our given line $y = 5x - 2$, the slope is $5$. This will also be the slope for our unknown line. We are given the point $(2, -1)$ and our slope $m = 5$. We now have the slope and a point on our unknown line. We can plug these values into the point-slope equation, which is given by the formula: $y - y_1 = m(x - x_1)$ Let's plug in the points and slope into the formula: $y - (-1) = 5(x - 2)$ Use distribution to simplify: $y + 1 = 5x + 5(-2)$ Simplify by multiplying: $y + 1 = 5x - 10$ To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we subtract $1$ from each side of the equation: $y = 5x - 10 - 1$ Add constants to simplify: $y = 5x - 11$ Now, we have the equation of the line in slope-intercept form.
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