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 328: 71


$y - 2 = x - 1$ $y = x + 1$

Work Step by Step

We are given the two points $(-2, -1)$ and $(1, 2)$. Let's use the formula to find the slope $m$ given two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in the values into this formula: $m = \frac{2 - (-1)}{1 - (-2))}$ Subtract the numerator and denominator to simplify: $m = \frac{3}{3}$ Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $3$: $m = 1$ Now that we have the slope, we can use one of the points and 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: $y - 2 = x - 1$ To change this equation into slope-intercept form, we need to isolate $y$. To isolate $y$, we add $2$ to each side of the equation: $y = x - 1 + 2$ Add the constants to simplify: $y = x + 1$ Now, we have the equation of the line in slope-intercept form.
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