Question

What is the equation of a line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6 ?

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Answer 1

y=\frac{1}{2}x-2

Explanation:

we are given

Line is perpendicular to y=−2x−6

we can compare it with

y=mx+b

where

m is slope

so, m=-2

so, slope is -2

Our line is perpendicular to this slope

so, slope of our line will be

`m'=-(1)/(-2)`

`m'=(1)/(2)`

now, we are given point as (6,1)

so,
`x_1=6,y_1=1`

now, we can use point slope form of line

`y-y_1=m(x-x_1)`

we can plug values

`y-1=(1)/(2)(x-6)`

now, we can solve for y

and we get

`y=(1)/(2)x-2`