Algebra 1: Common Core (15th Edition)

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

Chapter 5 - Linear Functions - 5-4 Point-Slope Form - Practice and Problem-Solving Exercises - Page 319: 19

Answer

$y = \frac{3}{2}x + \frac{5}{2}$

Work Step by Step

We are given the points $(1, 4)$ and the point $(-1, 1)$. 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: $m = \frac{1 - 4}{-1 - 1}$ Subtract the numerator and denominator to simplify: $m = \frac{-3}{-2}$ Divide the numerator and denominator by $-1$: $m = \frac{3}{2}$ 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: $y - 4 = \frac{3}{2}(x - 1)$ Use distribution to simplify: $y - 4 = \frac{3}{2}x - \frac{3}{2}$ To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we add $4$ to each side of the equation: $y = \frac{3}{2}x - \frac{3}{2} + 4$ Change $4$ into an equivalent fraction that has $2$ as its denominator so that both fractions have the same denominator: $y = \frac{3}{2}x - \frac{3}{2} + \frac{8}{2}$ Add the fractions to simplify: $y = \frac{3}{2}x + \frac{5}{2}$ Now, we have the equation of the line in slope-intercept form.
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