## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 3 - Parallel and Perpendicular Lines - 3-7 Equations of Lines in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 194: 28

#### Answer

$y - 5 = \frac{1}{4}(x - 3)$

#### Work Step by Step

We are given the points $(-5, 3)$ and $(3, 5)$. Let's use the formula to find the slope $m$ given two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Let's plug in the values into this formula: $m = \frac{5 - 3}{3 - (-5)}$ Subtract the numerator and denominator to simplify: $m = \frac{2}{8}$ Divide the numerator and denominator by their greatest common denominator, which is $2$: $m = \frac{1}{4}$ 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: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. Let's plug in the points and slope into the formula: $y - 5 = \frac{1}{4}(x - 3)$ This equation is now in point-slope form.

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