Draw the graph of 5x + 6y - 30 = 0 and use it to find the area of the triangle formed by the line and coordinate axes.

The above equation, 5x + 6y - 30 = 0 can be written as :

⇒ 6y = -5x + 30

⇒ y = $\dfrac{1}{6}(-5x + 30)$

⇒ y = $-\dfrac{5x}{6} + 5$.

When x = 0, y = -$\dfrac{(5 \times 0)}{6} + 5$ = 0 + 5 = 5,

x = 6, y = -$\dfrac{5 \times 6}{6} + 5$ = -5 + 5 = 0,

x = 12, y = -$\dfrac{5 \times 12}{6}$ + 5 = -10 + 5 = -5.

Table of values :

Steps of construction :

1. Plot the points (0, 5), (6, 0) and (12, -5) 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 = 6 units, Height = 5 units.

Area = $\dfrac{1}{2} \times 6 \times 5 = 15$ sq. units.

Hence, the graph of the given equation is shown in the adjoining figure and area of triangle = 15 sq. units.