# equation of the line

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• Dec 22nd 2009, 11:42 PM
jay1
equation of the line
Can you help me find the equation of the line perpendicular to the line x=4, and passing through the point (4, 2)?
• Dec 23rd 2009, 12:52 AM
Joel
The equation x = 4 has a gradient that is undefined.

The perpendicular to this line would be 0, so

using the point slope form of an equation at the point (4,2)

y - y1 = m (x- x1)

y - 2 = 0 (x - 4)

y - 2 = 0

y = 2 is the equation of the line perpendicular to x = 4 at the point (4, 2)
• Dec 23rd 2009, 01:14 AM
Bacterius
Joel, be more careful in the choice of your words :
Quote:

The perpendicular to this line would be 0, so
is meaningless, and more confusing than ever for someone trying to understand line equations.

The slope of the perpendicular to this line equals 0, so
• Dec 23rd 2009, 02:56 AM
HallsofIvy
Quote:

Originally Posted by jay1
Can you help me find the equation of the line perpendicular to the line x=4, and passing through the point (4, 2)?

The line x= 4 is vertical, parallel to the y axis so x is not changing.

The line perpendicular to it is horizontal, parallel to the x axis so y is not changing. Since y= 2 at the point (4, 2) and y is not changing, the equation is y= 2.
• Dec 23rd 2009, 02:57 AM
HallsofIvy
Quote:

Originally Posted by Joel
The equation x = 4 has a gradient that is undefined.

The perpendicular to this line would be 0, so

The gradient of the line perpendicular to this line would be 0.

Quote:

using the point slope form of an equation at the point (4,2)

y - y1 = m (x- x1)

y - 2 = 0 (x - 4)

y - 2 = 0

y = 2 is the equation of the line perpendicular to x = 4 at the point (4, 2)