Question

Consider the line y = - 4x +3,

Find the equation of the line that is parallel to this line and passes through the point (2, -3).

Answer 1

y = -4x + 5 {slope-intercept form}

Explanation:

y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂

{Two lines are parallel if their slopes are equal}

y = - 4x + 3 ⇒ m₁ = -4 ⇒ m₂ = -4

The point-slope form of the equation of a line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

m = -4

(2, -3) ⇒ x₁ = 2, y₁ = -3

point-slope form:

y - (-3) = -4(x - 2)

y + 3 = -4x + 8 {subtact 3 from both sides}

y = -4x + 5 ← slope-intercept form