Question

Determine the slope of the lines parallel and perpendicular to -4x+3y=11

Answer 1

`(4)/(3)` and -
`(3)/(4)`

Explanation:

The equation of a line in slope- intercept form is

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

Given

- 4x + 3y = 11 ( add 4x to both sides )

3y = 4x + 11 ( divide all terms by 3 )

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

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

Parallel lines have equal slopes, thus

slope of parallel line =
`(4)/(3)`

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

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

Answer 2

parallel = 4/3

perpendicular =-3/4

Explanation:

Solve for y

-4x+3y=11

Add 4x to each side

3y = 4x+11

Divide by 3

y = 4/3 x +11/3

This is in the form y = mx+b where m is the slope

m =4/3

The parallel line has the same slope

parallel slope is 4/3

The perpendicular line has a negative reciprocal slope

m = -(1 /4/3) = - 3/4