Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 3 - Parallel and Perpendicular Lines - 3-7 Equations of Lines in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 195: 45


$y = -x + 2$

Work Step by Step

We are given the line $y + 2 = -(x - 4)$. This equation is in point-slope form, which is given by the formula: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. However, we want this line in slope-intercept form. The first thing we want to do is use the distributive property to get rid of the parentheses: $y + 2 = -(x) - (-4)$ Multiply to simplify the equation: $y + 2 = -x + 4$ The slope-intercept form is given by the equation: $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept of the line. Therefore, with the slope-intercept form, we need to isolate $y$. We do this by subtracting $2$ from each side of the equation: $y + 2 - 2 = -x + 4 - 2$ Add or subtract to simplify: $y = -x + 2$ This line is now rewritten in slope-intercept form.
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