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Q10.

Expert-verified
Found in: Page 409

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Write $2x-3y=3$ 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 1. Given Information

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

## 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:

$\begin{array}{c}2x-3y=3\left(\text{Given equation}\right)\\ 2x-2x-3y=3-2x\left(\text{Subtracting}2x\text{from both sides}\right)\\ -3y=-2x+3\\ \frac{-3y}{-3}=\frac{-2x}{-3}+\frac{3}{-3}\left(\text{Dividing both sides by}-3\right)\\ y=\frac{2}{3}x-1\end{array}$

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 $\left(0,-1\right)$.

## 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 $y=\frac{2}{3}x-1$.