Algebra 1: Common Core (15th Edition)

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

Chapter 5 - Linear Functions - 5-3 Slope-Intercept Form - Lesson Check - Page 311: 2


$y = -x + 1$

Work Step by Step

First, we want to find the slope of this equation using the following formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $m$ is the slope and $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. Let's plug in our two points into this formula: $m = \frac{-1 - 4}{2- (-3)}$ Simplify by adding or subtracting in the numerator and denominator: $m = \frac{-5}{5}$ Simplify by dividing both the numerator and denominator by their greatest common factor, $5$: $m = -1$ Since we have the slope and two points, we can use the point-slope form, which is given by the following formula: $y - y_1 = m(x - x_1)$ Let's plug in the slope and a point into this formula: $y - 4 = -1(x - (-3))$ Simplify the right side of the equation: $y - 4 = -1(x + 3)$ Use the distributive property on the right side of the equation: $y - 4 = -x - 3$ This would be the point-slope form of the equation, but we want the slope-intercept form, so we need to isolate $y$ on the left side of the equation by adding $4$ to both sides of the equation: $y = -x + 1$
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