Question

For the linear equation, given above, draw the graph and then use the graph drawn (in the following case) to find the area of a triangle enclosed by the graph and the co-ordinates axes:

3x − (5 − y) = 7

Answer 1

First draw the graph as follows:

Simplify the given equation

3x − (5 − y) = 7

3x − 5 + y = 7

3x + y = 12

To plot the graph, we need x-intercept and y-intercept.

When y = 0:

3x = 12 ⟹ x = 4

So, the x-intercept = (4, 0)

When x = 0:

y = 12

So, the y-intercept = (0, 12)

O(0, 0), A(4, 0), B(0, 12)

Area of triangle OAB:

Area `= 1/2` × base × height

Base = OA = 4 units

Height = OB = 12 units

Area `= 1/2` × 4 × 12

= 24