Question

Draw the graph of the following equations :
3x + 2y + 6 = 0
3x + 8y - 12 = 0
Also, determine the co-ordinates of the vertices of the triangle formed by these lines and x-axis.

Answer 1

3x + 2y + 6 = 0  ...(1)
3x + 8y - 12 = 0 ...(2)

3x + 2y = -6
⇒ 3x = -6 - 2y
Corresponding values of x and y can be tabulated as :

x	-2	0	-2.66
y	0	-3	1

Plotting points (-2, 0), (0, 3), (-2.66, 1) and joining them, we get a line l₁ which is the graph of equation (1).

3x + 8y - 12 = 0
⇒ 3x = 12 - 8y
Corresponding values of x and y can be tabulated as :

x	4	-4	0
y	0	3	1.5

Plotting points (4, 0), (-4, 3), (0, 1.5) and joining them, we get a line l₂ which is the graph of equation (2).
It can be seen that the two lines l₁ and l₂ and the x-axis from a triangle ABC.

The coordinates of the vertices of ΔABC are A(-4, 3), B(-2, 0) and C(4, 0).