How to find the equation of a line perpendicular to another?

How does y+2=0 rearrange to y=-2? And how do you find a perpendicular line (with a given coordinate)?

a = 0,1

b = 10,6

Equation = y=1/2x+1

Find the equation of the line perpendicular to AB passing through B.

Please explain all in a 'step-to-step' fashion in the simplest way possible including any rearranging equations etc.

I know the answer (y=-2x+26) but, other than the negative reciprocal, I'm not sure how to get it. My answer on the exam was 'y=-2x+6' so I went wrong at the end.

Thanks a lot!

Re: How to find the equation of a line perpendicular to another?

Re: How to find the equation of a line perpendicular to another?

Ah, understood, thanks.

I can't catch on the last bit. Is there an easier way or could you explain how you got to that?

Re: How to find the equation of a line perpendicular to another?

Re: How to find the equation of a line perpendicular to another?

I'm really sorry but I still can't understand it. Where did -6 come from? Where did -10 come from? Why was the '-2' moved?

Could you explain the format of the above expressions please? And what is this 'point-slope formula'? y=mx+c or?

Re: How to find the equation of a line perpendicular to another?

The point-slope formula states that given the point on a line and the slope , then the equation of the line is:

The -2, which is the slope, was distributed to both terms within the parentheses.

Re: How to find the equation of a line perpendicular to another?

I understand now, but is there another way to do it? I don't think I'll remember that. I have trouble remembering that a line sloping to the left is +ve and to the right -ve (not even sure that's correct)

Or is there any way to relate that formula to y=mx+c? Or is there another formula altogether? I know how to get the slope, so is there another way to get the y intercept (c)?

Re: How to find the equation of a line perpendicular to another?

Yes, use the formula for slope with the points (10,6) and (0,*c*):

Re: How to find the equation of a line perpendicular to another?

My friend taught me an easier way. Substitute 'y' and 'x' with the coords of the point it passes through (B)

6=-2(10)+C

6=-20+C

26=C

Thanks for the help though!