How do you graph \[x+3y=9\]?

Hint: Here, in this problem, we have to graph the given equation. So, we have to find x-intercept and y-intercept with the given equation. We already know that for x-intercept the value of y is 0 and for y-intercept the value of x is 0, using this we can find the x and y coordinates and can plot the coordinate points in the graph.

Complete step by step answer:
We know that the given equation is,
\[x+3y=9\]……… (1)
Now we have to find x-coordinate.
We know that at x-intercept, y is equal to 0, substituting y = 0 in equation (1), we get
\[\begin{align}
  & \Rightarrow x+3\left( 0 \right)=9 \\
 & \Rightarrow x=9 \\
\end{align}\]
Therefore, the x coordinate is \[\left( 9,0 \right)\].
Now we have to find the y-coordinate.
We know that at y-intercept, the value of x is 0, substituting x = 0 in equation (1), we get
\[\Rightarrow 0+3y=9\]
We can divide by 3 on both sides, we get
\[\begin{align}
  & \Rightarrow \dfrac{3y}{3}=\dfrac{9}{3} \\
 & \Rightarrow y=3 \\
\end{align}\]
Therefore, the y-coordinate is \[\left( 0,3 \right)\].
We can also find other two points to be plotted by assuming value to x and y.
We can assume for y = 1, then the value of x from equation (1) is,
\[\begin{align}
  & \Rightarrow x+3\left( 1 \right)=9 \\
 & \Rightarrow x=6 \\
\end{align}\]
We can assume for y = 2, then the value of x from equation (1) is,
\[\begin{align}
  & \Rightarrow x+3\left( 2 \right)=9 \\
 & \Rightarrow x=3 \\
\end{align}\]
Therefore, the other two points are \[\left( 6,1 \right),\left( 3,2 \right)\]
Now we can plot the x-coordinate \[\left( 9,0 \right)\], y-coordinate \[\left( 0,3 \right)\] and other points \[\left( 6,1 \right),\left( 3,2 \right)\]


Note: Students make mistakes while finding x-intercept and y-intercept, we should always remember that, at x-intercept, the value of y is 0 and at y-intercept, the value of x is 0. We can assume any other points to find other points to be plotted in the graph.