Algebra 1: Common Core (15th Edition)

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

Chapter 5 - Linear Functions - 5-3 Slope-Intercept Form - Practice and Problem-Solving Exercises - Page 313: 60


$a = -5$

Work Step by Step

The equation is already in slope intercept form, which is given by the formula: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We can see that the coefficient of the variable $x$ would be the slope. We set this coefficient equal to the slope $m$ that we are given: $-\frac{1}{2}a = \frac{5}{2}$ Let's solve for $a$ by dividing both sides by $-\frac{1}{2}$. Dividing by a fraction means multiplying by its reciprocal; therefore, we multiply each side by the reciprocal of $-\frac{1}{2}$ or $-2$: $a = -2(\frac{5}{2})$ Multiply to simplify: $a = -\frac{10}{2}$ Simplify the fraction: $a = -5$
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