How do you graph $ 3x + 2y = 6 $ by plotting points?

Hint: In order to graph the above equation, consider the fact the graph to any linear function of the form $ ax + by + c = 0 $ is always a straight line ..As to plot a straight line we require two points. One point is the x-intercept obtained by putting $ y = 0 $ and another is the y-intercept obtained by putting $ x = 0 $ in the equation. By plotting, these two points and connect them to obtain the straight line of the equation.

Complete step-by-step answer:
We are given a linear equation in two variables $ x\,and\,y $ i.e. $ 3x + 2y = 6 $
As we know the graph to a linear function of the form $ ax + by + c = 0 $ is always a straight line.
So, in order to draw a line, we must have at least two points on the graph which we can connect to form a line.
We’ll be taking one point as y-intercept and another as x-intercept .
To calculate y-intercept of the graph, put $ x = 0 $ in the equation
\[
  3x + 2y = 6 \\
  3\left( 0 \right) + 2y = 6 \\
  2y = 6 \\
  y = \dfrac{6}{2} \\
  y = 3 \\
 \]
We get y-intercept at point $ \left( {0,3} \right) $
Now To calculate x-intercept of the graph, put $ y = 0 $ in the equation
\[
  3x + 2y = 6 \\
  3x + 2\left( 0 \right) = 6 \\
  3x = 6 \\
  x = \dfrac{6}{3} \\
  x = 2 \;
 \]
We get x-intercept at point $ \left( {2,0} \right) $


Now the graph the equation, we are jumping on the cartesian plan and plot $ \left( {0,3} \right) $ , $ \left( {2,0} \right) $ .Joining these two points we get a straight line representing our equation $ 3x + 2y = 6 $
Graph of equation having y-intercept as $ \left( {0,3} \right) $ and x-intercept as $ \left( {2,0} \right) $ .


Note: 1.Draw the cartesian plane only with the help of straight ruler and pencil to get the perfect and accurate results.
2.Mark the points carefully.
3. x-intercept is the point at which the line intersects the x-axis of the plane and similarly y-intercept is the point at which line intersects the y-axis of the plane.