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

3x - y = 6

Explanation:

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Answer 2

3x - y = 6

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + 3y = 21 ( subtract x from both sides )

3y = - x + 21 ( divide all terms by 3 )

y = -
`(1)/(3)` x + 7 ← in slope- intercept form

with slope m = -
`(1)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(3) )` = 3 , thus

y = 3x + c ← is the partial equation

To find c , substitute (1, - 3) into the partial equation

- 3 = 3 + c ⇒ c = - 3 - 3 = - 6

y = 3x - 6 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 6 ( add 6 to both sides )

6 = 3x - y , that is

3x - y = 6 ← in standard form