Draw the graph of 3x + 2y = 6. Use the graph drawn to find the area of triangle formed by the line drawn and the co-ordinate axes.

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then 3 $\times$ 0 + 2y = 6 ⇒ y = 3

Let x = 2, then 3 $\times$ 2 + 2y = 6 ⇒ y = 0

Let x = 4, then 3 $\times$ 4 + 2y = 6 ⇒ y = -3

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

The area of the triangle = $\dfrac{1}{2}$ x base x height

= $\dfrac{1}{2}$ x OA x OB

= $\dfrac{1}{2}$ x 2 x 3

= $\dfrac{6}{2}$ sq. units

= 3 sq. units

Hence, the area of triangle formed by the line drawn and the co-ordinate axes is 3 sq. units.