## 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: 30

#### Answer

$y - 8 = \frac{3}{5}(x - 5)$

#### Work Step by Step

We are given the points $(0, 5)$ and $(5, 8)$. 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 these values into this formula: $m = \frac{8 - 5}{5 - 0}$ Subtract the numerator and denominator to simplify: $m = \frac{3}{5}$ 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: $y - y_1 = m(x - x_1)$, 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: $y - 8 = \frac{3}{5}(x - 5)$ This equation is now in point-slope form.

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