Question

How do you graph $ 3y + 4x = 12? $

Answer 1

Hint: To draw the graph of the given equation of a straight line, since this equation consists of a constant term so its graph will definitely have $ x\;{\text{and}}\;y $ intercepts. So go with the intercept method to plot a graph, in which you have to find the $ x\;{\text{and}}\;y $ intercepts of the graph then plot them on a graph paper and then join the intercepts and extend the line to get the required graph. To get $ x $ intercept put $ y = 0 $ in the given equation and solve for $ x $ and do vice versa for $ y $ intercept.

Complete step-by-step answer:
In order to graph the given equation $ 3y + 4x = 12 $ we will go through the intercept method to draw a graph. In the intercept method, we find the $ x\;{\text{and}}\;y $ intercepts of the graph first and then plot them on a graph paper and join and extend them to get the required graph.
So first finding the $ x $ intercept by putting $ y = 0 $ in the equation $ 3y + 4x = 12 $ , we will get
 $
   \Rightarrow 3 \times 0 + 4x = 12 \\
   \Rightarrow 4x = 12 \\
   \Rightarrow x = \dfrac{{12}}{4} = 3 \\
  $
Similarly calculating $ y $ intercept, we will get
 $
   \Rightarrow 3y + 4 \times 0 = 12 \\
   \Rightarrow 3y = 12 \\
   \Rightarrow y = \dfrac{{12}}{3} = 4 \;
  $
Therefore coordinates of $ x\;{\text{and}}\;y $ can be written as $ (3,\;0)\;{\text{and}}\;(0,\;4) $ respectively.
Plotting these coordinates of $ x\;{\text{and}}\;y $ intercepts on a graph paper, we will get

Now joining the intercept points and extending it, we will get

Therefore this is the required graph of the given equation.

Note: You can also solve this question or draw a graph of the given equation with help of plotting-points method which is considered as the parent method of the intercept method. Intercept method is a special case of plotting points method in which we put the value of the variable equals zero. And also plotting points method can be used in graphing of all types of straight line equations.