Question

Write the equation of the line that is perpendicular to 3x + 7y = 15 and passes through (4, 9)

Answer 1

7x - 3y = 1

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 3x + 7y = 15 into this form

Subtract 3x from both sides

7y = - 3x + 15 ( divide all terms by 7 )

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

with slope m = -
`(3)/(7)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(7) )` =
`(7)/(3)`, thus

y =
`(7)/(3)` x + c ← is the partial equation of the line

To find c substitute (4, 9) into the partial equation

9 =
`(28)/(3)` + c ⇒ c -
`(1)/(3)`

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

Multiply through by 3

3y = 7x - 1 ( subtract 3y from both sides )

0 = 7x - 3y - 1 ( add 1 to both sides )

1 = 7x - 3y, that is

7x - 3y = 1 ← in standard form