Question

Draw the graph of two lines, whose equations are 3x-2y+6=0 and x+2y-6-0 on the same graph paper.
(12 sq units)
Find the area of triangle formed by two lines and x-axis​

Answer 1

Explanation:

Given : Equations of the line 3x + 2y - 6 = 0 and x + 2y - 6 = 0

To Find : Area of the triangle formed by 2 lines and x-axis.

Solution:

Equation of the first line is 3x + 2y - 6 = 0

Slope-intercept form of the equation is,

2y = -3x + 6

y=\frac{-3}{2}x+3y=

2

−3

x+3 ---------(1)

Table for input-output values will be,

x 0 2 4

y 3 0 -3

Similarly, second equation is,

x + 2y - 6 = 0

2y = -x + 3

y = -\frac{1}{2}x+3−

2

1

x+3 --------(2)

Table for input-output values will be,

x 0 2 6

y 3 2 0

Now by plotting these points we get a triangle with vertices (0, 3), (2, 0) and (6, 0)

Area of the given triangle = \frac{1}{2}(\text{base})(\text{height})

2

1

(base)(height)

Base = 4 units

Height = 3 units

Area = \frac{1}{2}(4)(3)

2

1

(4)(3) = 6 square units