How do you graph the equation by plotting points $3x+5y=12$ ?

Hint: To graph the above equation $3x+5y=12$, we are going to first put x as 0 in this equation and then solve the equation to find the value of y. Let us assume this point as A. Now, we are going to put the value of y as 0 in the above equation and then solve the equation to find the value of x. And mark this point as B. Now, plot these points A and B on the graph and join these two points to get the straight line.

Complete step-by-step answer:
The equation given in the above problem which we have to plot is as follows:
$3x+5y=12$
Now, let us put the value of x as 0 in the above equation we get,
$\begin{align}
  & \Rightarrow 3\left( 0 \right)+5y=12 \\
 & \Rightarrow 0+5y=12 \\
 & \Rightarrow 5y=12 \\
\end{align}$
Dividing 5 on both the sides of the above equation we get,
$\begin{align}
  & \Rightarrow \dfrac{5y}{5}=\dfrac{12}{5} \\
 & \Rightarrow y=\dfrac{12}{5} \\
\end{align}$
Hence, from the above, we have got one point which we are going to plot on the graph as $\left( 0,\dfrac{12}{5} \right)$. Let us call this point as A. Now, we are plotting this point A on the graph.

Now, let us substitute y as 0 in the above equation we get,
$\begin{align}
  & \Rightarrow 3x+5\left( 0 \right)=12 \\
 & \Rightarrow 3x+0=12 \\
\end{align}$
Dividing 3 on both the sides of the above equation we get,
$\begin{align}
  & \Rightarrow \dfrac{3x}{3}=\dfrac{12}{3} \\
 & \Rightarrow x=4 \\
\end{align}$
From the above, we got the second point as $\left( 4,0 \right)$ and let us denote this point as B. Now, we are going to plot this point B (4, 0) on the graph and we get,

Now, we are going to join these two points A and B to draw the straight line equation.

Hence, we have drawn the straight line which is having equation $3x+5y=12$.

Note: The information you can get from the above graph is the x intercept which is the point on the x axis where the straight line is cutting the x axis and y intercept is the point on the y axis where the equation of a straight line is cutting.
So, in the graph, we have drawn above i.e.:

Point B is the x intercept and point A is the y intercept.