Geometry
posted by Unknown on .
1. Why do you think that the slope of a vertical line is called "undefined?"
2. Can you find the equation of a line if you are given the slope and the xintercept? If so, explain how. If not, explain why you can't.

Consider any two points that form a vertical line,
e.g. (x, a) and (x, b)
slope = (ba)/(xx)
= (ba)/0 , but division by zero is "undefined"
Thus the slope of a vertical line is undefined.
2. Yes, given the slope m and the xintercept we can find the equation of the line
e.g. slope = 4 , xintercept is (3,0)
y = 4x + b
but (3,0) lies on it, so
0 = 4(3) + b
b = 12
y = 4x  12
in general if the slope is m and the xintercept is k
the equation is
y = m(xk)
for the above, y = 4(x3)
which expands to y = 4x  12 , as above.