perpendicular lines

Question

Find the equation of the line that is perpendicular to the line -x+3y=-1 and goes through the point (4,-2)

Answer 1

-x + 3y = -1

 

solve for y:

 

3y = x - 1

 

divide both sides by 3:

 

3y/3 = (x - 1)/3

 

y = (1/3)x - 1/3        this is in the form y = mx + b. m is the slope and b is the y-intercept

 

any line perpendicular to the given line will have a slope of -1/m. In this case (-1/(1/3)), which equals -3.

 

use y - y₁ = m(x - x₁), given (x₁ = 4, y₁ = -2)

 

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

 

y + 2 = -3x + 12

 

y = -3x + 12 - 2

 

y = -3x + 10