Question

Draw the graph of the following lines: y = x + 2 and 5x + 3y = 30.

Find their point of intersection and the area of triangle formed by the two lines with x-axis.

Answer 1

Given:

y = x + 2

5x + 3y = 30

5x + 3(x + 2) = 30

5x + 3x + 6 = 30

8x = 24

x = 3

y = 3 + 2 = 5

Intersection point = (3, 5)

y = 0 ⇒ x + 2 ⇒ x = −2 ⇒ Point A = (–2, 0)

y = 0 = 5x = 30 = x = 6 ⇒ Point B = (6, 0)

Vertices: A(–2, 0), B(6, 0), C(3, 5)

Base = ∣6 − (–2)∣ = 8

Height = 5
Area = `1/2  xx "base" xx "height"`

Area = `1/2 xx 8 xx 5`

20 square units