Draw the graph of 4x - 3y + 12 = 0 and use it to find the area of the triangle formed by the line and co-ordinate axes. Take 2 cm = 1 unit on both axes.

The above equation, 4x - 3y + 12 = 0 can be written as :

⇒ 3y = 4x + 12

⇒ y = $\dfrac{4}{3}x + 4$

When x = -6, y = $\dfrac{4}{3} \times -6 + 4$ = -8 + 4 = -4,

x = -3, y = $\dfrac{4}{3} \times -3 + 4 =$ -4 + 4 = 0,

x = 0, y = $\dfrac{4}{3} \times 0 + 4 =$ 0 + 4 = 4.

Table of values :

Steps of construction :

1. Plot the points (-6, -4), (-3, 0) and (0, 4) on the graph.

2. Connect any two points by a straight line.

Observe that the third point lies on the straight line.

By formula,

Area of triangle = $\dfrac{1}{2} \times \text{ base} \times \text{ height}$

From graph,

Base = 3 units, Height = 4 units.

Area = $\dfrac{1}{2} \times 3 \times 4 = 6$ sq. units.

Hence, the graph of the given equation is shown in the adjoining figure and area of triangle = 6 sq. units.