Question

Graph the equation. Tell whether the equation is a function.

$x-3y=-9$

Short answer

The function form of the equation is $y=\frac{1}{3}x+3$.

Step-by-step solution

Step 1. Given information.

The given equation is $x-3y=-9$.

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:

$\begin{array}{c}x-3y=-9\left(\text{Givenequation}\right)\\ x-x-3y=-9-x\left(\text{Subtracting}x\text{frombothsides}\right)\\ -3y=-x-9\\ \frac{-3y}{-3}=\frac{-x}{-3}-\frac{9}{-3}\left(\text{Dividingbothsidesby}-3\right)\\ y=\frac{1}{3}x+3\end{array}$

Therefore, the function form of our given equation would be $x-3y=-9$.

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

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

Step 3. Conclusion.

The above graph is the required graph.