Question

What is an equation of the line that passes through the point (1,3) and is

perpendicular to the line x + 3y = 9?

Answer 1

y = 2x + 0

y = mx + C - equation of the line

Explanation:

First, find the slope

x + 3y = 9

Using the equation of line

y = mx + C

3y = 9 - x

3y = -x + 9

Divide both sides by 3

3y / 3 = ( -x + 9) / 3

y = ( -x + 9) / 3

We can separate it

y = -x/3 + 9/3

y = -x/3 + 3

m = -1/3

Slope = -1/3

Since weve gotten our slope

Let's use the equation of point slope form

y - y_1 = m(x - x_1)

We are provided with a point

( 1, 3)

x_1 = 1

y_1 = 3

If two lines are perpendicular, their slope will be negative reciprocal

m = -1/3

Perpendicular = +3/1

insert the values

y - 3 = 3(x - 1)

y - 3 = 3x - 3

y = 3x - 3 + 3

-3 cancels +3

y = 3x + 0