Question 552413
An equation in slope-intercept form is:  y = mx + b.
m = slope = the 'rise' over the 'run' or the change in y divided by the change in x.
(0,b) = y-intercept
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The statement "with an undefined slope" has a distinct mathematical meaning:  it means you have a situation where you need to divide by 0.
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In contrast, 0 can be divided by any number, which yields 0 as the answer.
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The slope = change in y divided by the change in x.
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slope = m = (y-y<sub>1</sub>) / (x-x<sub>1</sub>)
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To divide by 0 would mean x = x<sub>1</sub>.
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That can only be a vertical line.
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The vertical line that goes through (3,-2) is simply:  x = 3.
This line goes through all of the points from (3, -infinity) to (3, +infinity), where y takes on any value from -infinity to +infinity.
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Interestingly, the horizontal line that goes through (3,-2) is simply: y = -2.  It has a slope = 0.
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Vertical and horizontal lines are special cases.