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Kaikerscupcake
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


calculista

Step [tex]1[/tex]

Find the slope of the line perpendicular to the given line

we have

the equation of the given line is

[tex]y=\frac{1}{2}x+7[/tex]

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

in this problem the slope m1 of the given line is

[tex]m1=\frac{1}{2}[/tex]

so

[tex]m2=-\frac{1}{m1}[/tex]

[tex]m2=-2[/tex]

Step [tex]2[/tex]

Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]

we know that

the equation of the line is

[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]

therefore

the answer is the option A

the equation of the line is [tex]y=-2x+14[/tex]

see the attached figure to better understand the problem

Ver imagen calculista

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