Question

Find an equation of the line, which is perpendicular to the line

3x −4y = 5 and passes through point P (1, −1).

Answer 1

4x + 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 )

given the line

3x - 4y = 5 ( subtract 3x from both sides )

- 4y = - 3x + 5 ( divide through by - 4 )

y =
`(3)/(4)` x -
`(5)/(4)` ← in slope- intercept form

with slope m =
`(3)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((3)/(4) )` = -
`(4)/(3)` , then

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

to find c substitute P (1, - 1 ) into the partial equation

- 1 = -
`(4)/(3)` (1) + c = -
`(4)/(3)` + c ( add
`(4)/(3)` to both sides )

`(1)/(3)` = c

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

multiply through by 3 to clear the fractions

3y = - 4x + 1 ( add 4x to both sides )

4x + 3y = 1 ← equation of perpendicular line in standard form