Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 3 - Parallel and Perpendicular Lines - 3-7 Equations of Lines in the Coordinate Plane - Practice and Problem-Solving Exercises - Page 196: 61


$a = 9$

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, $y = \frac{2}{9}ax + 6$, then $\frac{2}{9}a$ would be $m$, our slope. We know that the actual value for our slope is $m = 2$, so we set $\frac{2}{9}a$ equal to $2$, and then solve for $a$: $\frac{2}{9}a = 2$ To solve for $a$, we divide both sides of the equation by $\frac{2}{9}$, which means that we multiply by the reciprocal, which is $\frac{9}{2}$: $(\frac{9}{2})(\frac{2}{9})a = 2(\frac{9}{2})$ Multiply to simplify: $a = \frac{18}{2}$ Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $2$: $a = 9$
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