math
posted by mota on .
parallel and perpendicular lines
Determine an equation of each of the following lines .
*the line perpendicular to y4=0 and passing through the point (1,6)
** the line perpendicular to 3x12y+16=0 and having the same yintercept as the line 14x13y52=0
and explain ....

Put y4 = o into the form
y = m x + b
y = 0 x + 4
now the slope of the line perpendicular to that is 1/m = 1/0 which is undefined so we will have to use our heads.
y = 4 is a horizontal line through y = 4, x = anything.
x = constant, any constant, is perpendicular to y = 4
So we want the vertical line x = 1
That line, x = 1 , passes through all values of y including 6

Now
3x 12 y + 16 = 0
12 y = 3 x + 16
y = (1/4)x + 4/3
what is slope of perpendicular?
m' = 1/(1/4) = 4
so the line we want is
y = 4 x + b
what is b?
well when x = 0, 13 y = 52
y = 52/13
so
52/13 = 4(0) + b
b = 52/13
so
y = 4x 52/13 
Y=1/4x+8