# Geometry

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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 x-intercept? If so, explain how. If not, explain why you can't.

• Geometry -

Consider any two points that form a vertical line,
e.g. (x, a) and (x, b)

slope = (b-a)/(x-x)
= (b-a)/0 , but division by zero is "undefined"

Thus the slope of a vertical line is undefined.

2. Yes, given the slope m and the x-intercept we can find the equation of the line
e.g. slope = 4 , x-intercept 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 x-intercept is k
the equation is
y = m(x-k)

for the above, y = 4(x-3)
which expands to y = 4x - 12 , as above.

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