Question

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

Short answer

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

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:

$\begin{array}{c}2x-3y=3\left(\text{Givenequation}\right)\\ 2x-2x-3y=3-2x\left(\text{Subtracting}2x\text{frombothsides}\right)\\ -3y=-2x+3\\ \frac{-3y}{-3}=\frac{-2x}{-3}+\frac{3}{-3}\left(\text{Dividingbothsidesby}-3\right)\\ y=\frac{2}{3}x-1\end{array}$

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