For the linear equation, given below, draw the graph and then use the graph drawn to find the area of a triangle enclosed by the graph and the co-ordinate axes :

3x - (5 - y) = 7

3x - (5 - y) = 7

Step 1:

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

Let x = -1, then 3 $\times$ (-1) - (5 - y) = 7 ⇒ y = 15

Let x = 0, then 3 $\times$ 0 - (5 - y) = 7 ⇒ y = 12

Let x = 1, then 3 $\times$ 1 - (5 - y) = 7 ⇒ y = 9

Let x = 4, then 3 $\times$ 4 - (5 - y) = 7 ⇒ y = 0

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 ABO will be = $\dfrac{1}{2} \times base \times$ altitude

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

= $\dfrac{1}{2} \times 4 \times$ 12 square unit

= 24 square unit

Hence, the area of triangle = 24 square unit.