Question

What is the equation of the line that passes through (3, –1) and is perpendicular to the line y = -3x +2 ?

Answer 1

EXPLANATION.

Equation of the line that passes through (3,-1).

Perpendicular to the line : y = - 3x + 2.

As we know that,

Slope of the perpendicular line : m = b/a.

Slope of the line : y + 3x - 2 = 0.

Slope of the line : 3x + y - 2 = 0.

Slope of the line : m = 1/3.

As we know that,

Formula of the equation of line.

⇒ (y - y₁) = m(x - x₁).

Put the value in the equation, we get.

⇒ (y - (-1)) = 1/3(x - 3).

⇒ (y + 1) = 1/3(x - 3).

⇒ 3(y + 1) = 1(x - 3).

⇒ 3y + 3 = x - 3.

⇒ x - 3 - 3y - 3 = 0.

⇒ x - 3y - 6 = 0.

                                                                                                                           

MORE INFORMATION.

Slope of a line.

(1) = m = tanθ, where θ is the angle made by a line with the positive direction of x axis in anticlockwise.

(2) = The slope of a line joining two points (x₁, y₁) and (x₂, y₂) is given by m = (y₂ - y₁)/(x₂ - x₁).