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Answers without the blur. Sign up and see all textbooks for free! Q31.

Expert-verified Found in: Page 410 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Write the equation in function form. Then graph the equation. $2x+3y=12$

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

See the step by step solution

## Step 1. Given Information.

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

## Step 2. Calculation.

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

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

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 $\left(0,4\right)$.

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 $y=-\frac{2}{3}x+4$. ### Want to see more solutions like these? 