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: 61


$a = \frac{3}{4}$

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: $\frac{3}{4}a = \frac{9}{16}$ Let's solve for $a$ by dividing both sides by $\frac{3}{4}$. Dividing by a fraction means to multiply by its reciprocal; therefore, we multiply each side by the reciprocal of $\frac{3}{4}$ or $\frac{4}{3}$: $a = (\frac{4}{3})(\frac{9}{16})$ Multiply to simplify: $a = \frac{36}{48}$ Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is $12$: $a = \frac{3}{4}$
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