Question

Consider the line
`y=(2)/(3) x+1`.

Find the equation of the line that is perpendicular to this line and passes through the point (-4, 5)

Find the equation of the line that is parallel to this line and passes through the point (-4, -5)

Equation of perpendicular:

Equation of parallel line:

Answer 1

we are given equation of line

`y=(2)/(3) x+1`

Equation of perpendicular line:

Firstly , we will find slope of line

`y=(2)/(3) x+1`

we can compare it with

y=mx+b

we get

`m=(2)/(3)`

we know that

slope of perpendicular line will be -1/m

so, slope is

`(-3)/(2)`

It passes through point (-4,5)

so, we can use point slope form of line

`y-5=-(3)/(2)(x+4)`

we get

`y=-(3)/(2)x-1`..........Answer

Equation of parallel line:

Firstly , we will find slope of line

`y=(2)/(3) x+1`

we can compare it with

y=mx+b

we get

`m=(2)/(3)`

we know that

slope of parallel line always equal

so, slope is

`(2)/(3)`

It passes through point (-4,-5)

so, we can use point slope form of line

`y+5=(2)/(3)(x+4)`

we get

`y=(2)/(3)x-(7)/(3)`............Answer