# Thread: If AB passes through the point (2,3) and is perpendicular to y= 2x-7, find the equati

1. ## If AB passes through the point (2,3) and is perpendicular to y= 2x-7, find the equati

If AB passes through the point (2,3) and is perpendicular to y= 2x-7, find the equation of AB in general form.
Please either provide the process of doing so, or help me work through it. Anything would be appreciated. I know it’s probably quite simple, but I can’t seem to understand this problem. Thank you for your help!

2. For 2 perpendicular lines, product of slopes is -1.

$m_1=2$
$m_2=-\frac{1}{2}$

Slope of AB is $-\frac{1}{2}$

$y=-\frac{1}{2}x+C$
This line passes through (2,3).
$3=-\frac{1}{2}*2+C$
$3=-1+C$
$C=4$

The equation of AB is $y=-\frac{1}{2}x+4$

3. ## A reply for Alex

Alex,

I do not understand what general form means. Apparently you have not given me the answer in general form, as I in fact have the answer, which is:

x+2y-8= 0

How do I obtain this answer?

4. Originally Posted by JadeKiara
Alex,

I do not understand what general form means. Apparently you have not given me the answer in general form, as I in fact have the answer, which is:

x+2y-8= 0

How do I obtain this answer?
Hmmm... This is strange. You are learning co-ordinate geometry, so you are expected to know basic algebra!

Is it hard to manipulate $y=-\frac{1}{2}x+4$ to get $x + 2y - 8 = 0$?

I guess you should review basic algebra first. That will help you a lot in Co-ordinate geometry.

5. Well, it is certainly strange to know that we have not done that in class. Maybe the teacher is attempting to challenge us? I do not know. I have researched the general form, and thus obtained the following formula: ax + by = C

Can you explain how to do this operation please?

6. $y=-\frac{1}{2}x+4$
Multiply throughout by 2
$2y=-x+8$
$x+2y-8=0$

7. Thank you Alex. It is beyond me why I have not learnt that, seeing as it is essential to do so. No wonder why I couldn't do it!

Anyway, I have researched the conversion of the two forms now, and hopefully I won't have that trouble in the future.

Thank you once again!