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Q31.

Expert-verified

Pre-algebra

Found in: Page 410

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Write the equation in function form. Then graph the equation.
$2 x + 3 y = 12$

The function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

An equation: $2 x + 3 y = 12$

Step 2. Calculation.

To write the given equation in function form, we need to convert our equation in slope-intercept form $(y = m x + b)$ as:

$\begin{matrix} 2 x + 3 y = 12 (Given equation) \\ 2 x - 2 x + 3 y = 12 - 2 x (Subtracting 2 x from both sides) \\ 3 y = - 2 x + 12 \\ \frac{3 y}{3} = \frac{- 2 x}{3} + \frac{12}{3} (Dividing both sides by 3) \\ y = - \frac{2}{3} x + 4 \end{matrix}$

Therefore, the function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

We can see that the slope of our given equation is $- \frac{2}{3}$ and the y-intercept is $(0, 4)$ .

Upon graphing our given equation, we will get our required graph as shown below:

Step 3. Conclusion.

The function form of our given equation would be $y = - \frac{2}{3} x + 4$ .

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