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Q10.

Expert-verified

Pre-algebra

Found in: Page 409

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 $2 x - 3 y = 3$ in function from. Then graph the equation.

The function form of our given equation would be $y = \frac{2}{3} x - 1$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given equation is $2 x - 3 y = 3$ .

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 = 3 (Given equation) \\ 2 x - 2 x - 3 y = 3 - 2 x (Subtracting 2 x from both sides) \\ - 3 y = - 2 x + 3 \\ \frac{- 3 y}{- 3} = \frac{- 2 x}{- 3} + \frac{3}{- 3} (Dividing both sides by - 3) \\ y = \frac{2}{3} x - 1 \end{matrix}

Therefore, the function form of our given equation would be $y = \frac{2}{3} x - 1$ .

We can see that the slope of our given equation is $\frac{2}{3}$ and the y-intercept is $(0, - 1)$ .

Step 3. Graph the obtained equation.

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

Step 4. Conclusion.

The above graph is the required graph and the form of the equation in function is $y = \frac{2}{3} x - 1$ .

Most popular questions for Math Textbooks

Write the equation in function form. Then graph the equation.

2 x + 3 y = 12

Tell whether the ordered pair is a solution of $3 x + 2 y = - 8$ .

$(- 2, - 1)$

draw a mapping diagram that represents a relation with domain $- 1, 0, 2$ and range 1, 4. Is only one answer possible? Explain.

Represent the relation as a graph and as a mapping diagram. Then tell whether the relation is a function. Explain your reasoning.

$(0, 4), (2, 0), (6, - 4), (- 4, 2), (8, 0)$

Tell whether the ordered pair is a solution of the equation.

$y = x - 3; (1, - 4)$

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