Question

Find a general equation of a line which passes through:
(i) (0, -5) and (3, 0) (ii) (2, 3) and (-1, 2).

Answer 1

We have the equation of a line which passes through (x₁,y₁) and (x₂,y₂) is
y - y₁ = `(y_2 - y_1)/(x_2 - x_1)(x - x_1)`
(i) Putting x₁ = 0, y₁ = -5 and x₂ = 3, y₂ = 0
y - (-5) = `(0 - (-5))/(3 - 0)(x - 0)`
⇒ y + 5 = `(5)/(3)(x - 0)`
⇒ 3y + 15 = 5x
⇒ 5x - 3y - 15 = 0
Which is the required equation.
(ii) Putting x₁ = 2, y₁ = 3 and x = -1, y₂ = 2
y - 3 = `(2 - 3)/(-1 - 2)(x - 2)`
⇒ y - 3 = `(-1)/(-3)(x - 2)`
⇒ 3y - 9 = (x - 2)
⇒ x - 2 - 3y + 9 = 0
⇒ x - 3y + 7 = 0
whoch is the equation of the required line.
⇒ 3y - 9 = (x - 2)
⇒ x - 2 - 3y + 9 = 0
⇒ x - 3y + 7 = 0
which is the equation of the required line.