Algebra 1: Common Core (15th Edition)

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

Chapter 5 - Linear Functions - 5-6 Parallel and Perpendicular Lines - Practice and Problem-Solving Exercises - Page 335: 45


$y = -\frac{2}{5}x + \frac{29}{5}$

Work Step by Step

We are given the points $(2, 5)$ and $(12, 1)$. 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: $m = \frac{1 - 5}{12 - 2}$ Subtract the numerator and denominator to simplify: $m = \frac{-4}{10}$ Divide the numerator and denominator by their greatest common denominator, which is $2$: $m = -\frac{2}{5}$ 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: $y - 5 = -\frac{2}{5}(x - 2)$ This equation is now in point-slope form. To change this equation into the point-intercept form, we need to isolate $y$. Use distribution to simplify: $y - 5 = -\frac{2}{5}x - \frac{2}{5}(-2)$ Simplify by multiplying: $y - 5 = -\frac{2}{5}x + \frac{4}{5}$ To isolate $y$, we add $5$ to each side of the equation: $y = -\frac{2}{5}x + \frac{4}{5} + 5$ Change $5$ into an equivalent fraction that has $5$ as its denominator so that both fractions have the same denominator: $y = -\frac{2}{5}x + \frac{4}{5} + \frac{25}{5}$ Add the fractions to simplify: $y = -\frac{2}{5}x + \frac{29}{5}$ Now, we have the equation of the line in slope-intercept form.
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