Question

What is the equation of the line that is perpendicular to the line and passes through the point (6, 2)?

Answer 1

Hey there! :D

So, when you find something perpendicular, you are finding the opposite reciprocal.

The slope is 1/2 because:

y=mx+b <== it is in this form; m is equal to slope.

Flip the 2 and 1 and make it negative.

2/1= -2

We already know "C" and "D" aren't the options. Now, we can just plug in the points given to see if it works. Plug in the set of points (6,2)

y=-2x+14

2=-2(6)+14

2=-12+14

2=2 <== this works. This is our answer. Let's just make sure by checking the other one.

y=-2x-2

2=-2(6)-2

2=-12-2

2=-14 <== that is not true.

The first option is correct.

I hope this helps!
~kaikers

Answer 2

Step
`1`

Find the slope of the line perpendicular to the given line

we have

the equation of the given line is

`y=(1)/(2)x+7`

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

`m1*m2=-1`

in this problem the slope m1 of the given line is

`m1=(1)/(2)`

so

`m2=-(1)/(m1)`

`m2=-2`

Step
`2`

Find the equation of the line with slope m2 and passes through the point
`(6, 2)`

we know that

the equation of the line is

`y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14`

therefore

the answer is the option A

the equation of the line is
`y=-2x+14`

see the attached figure to better understand the problem