Question

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

perpendicular to the line x + 3y
= 21?

Answer 1

1. -3x +y = -6 or y = 3x -6

Explanation:

Arrange values into slope intercept form ; y=mx+b

`x +3y = 21\\3y = -x +21\\3y/3 = -x/3 +21/3\\\\y = -1/3 x + 7`

`(1, -3) =(x ,y)\\\\y =-(1)/(3)x + 7\\\\m = -(1)/(3) \\\\m_2=-1/m_1\\\\m_2 =(-1)/(-(1)/(3) ) \\\\m_2=3\\`

Arrange values into slope - intercept form and solve for b

`-3 = 3(1 )+ b\\-3 = 3 +b\\-3-3=b\\-6 =b\\\\b=-6\\m =3`

Substitute new values into slope intercept form

`y = 3x -6`

Arrange in standard form

`-3x +y = -6`

Answer 2

3x -y = 6

Explanation:

When the equation of a line is given in the form ax+by=c, the perpendicular line through point (h, k) will be ...

bx -ay = bh -ak

Here, we have a=1, b=3, h=1, k=-3, so the line is ...

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

3x -y = 6