what is the point slope formula?

Question

write the eqn. of a line that passes through (-2,2) and is perpendicular to a line that contains (1,3) and (4,2).

Answer 1

The points are (1, 3), and (4, 2).

Slope of a line through two points (m )  = (y₂ - y₁ ) / (x₂ - x₁ ).

Substitute the values of (x₁, y₁) = (1, 3) and (x₂, y₂) = (4, 2) in (y₂ - y₁) / (x₂ - x₁).

m = (2 - 3 )/(4 - 1)

m = - 1/3.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line through (- 2, 2) is 3/1 (or) 3.

To find the y - intercept of perpendicular line, substitute the values of

(x, y) = (- 2, 2) and m = 3 in the slope - intercept from: y = mx + b and solve for b.

2 = 3(- 2) + b

2 = -6 + b

b - 6 = 2

b = 2 + 6 = 8.

Substitute the values of m = 3 and b = 8 in the slope - intercept form of equation

y = mx + b ⇒ y = 3x + 8.

The equation of perpendicular line is y = 3x + 8.