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 ?

Answer 1

Answer:

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

Step-by-step 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

$m'=-\frac{1}{-2}$

$m'=\frac{1}{2}$

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

$y-1=\frac{1}{2}(x-6)$

now, we can solve for y

and we get

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