## 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 196: 63

#### Answer

$a = \frac{1}{6}$

#### Work Step by Step

This equation is in slope-intercept form, which is given by the formula: $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept of the line. If we look at the equation we are given, $y = -4ax - 10$, then $-4a$ would be $m$, our slope. We know that the actual value for our slope is $m = -\frac{2}{3}$, so we set $-4a$ equal to $-\frac{2}{3}$, and then solve for $a$: $-4a = -\frac{2}{3}$ To solve for $a$, we divide both sides of the equation by $-4$, which means that we multiply by the reciprocal, which is $-\frac{1}{4}$: $(-\frac{1}{4})(-4)a = (-\frac{1}{4})(-\frac{2}{3})$ Multiply to simplify: $a = \frac{2}{12}$ Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $2$: $a = \frac{1}{6}$

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