Question

Find the Equation of the Perpendicular Line

Instructions: Find the equation of the line through point (-1, 2) and perpendicular to x + 3y = 3.

y =

Answer 1

y = 3x +5

Explanation:

The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.

Coefficients swapped

The desired equation in the given standard form will be ...

3x -y = c . . . . . . for some new constant c

Note that we have kept the x-coefficient positive, and have negated the y-coefficient.

Constant value

The new constant will make the equation true at the point (-1, 2):

3(-1) -(2) = c = -5

So, the standard-form equation is ...

3x -y = -5

Slope-intercept form

The answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:

3x -y +(y+5) = -5 +(y+5)

3x +5 = y

y = 3x +5