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Question 120269: How do you find an equation for a line that has an unidentified slope?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! First thing, do you mean 'unidentified' or 'undefined'?
If you mean 'undefined,' then you are dealing with a vertical line. Find any point on the line and set x equal to the x-coordinate of that point. For example, if you have a line with an undefined slope passing through the point (3,5), then the equation of the line is  . The slope of a vertical line is undefined because if you try to compute the slope, you end up with a zero denominator. Looking at it another way using the example here, another way to write  is  . Now if you try to put this into slope-intercept form you get:
 giving you an undefined slope and an undefined intercept because you are dividing by zero.
On the other hand, if you actually meant 'unidentified,' then you must know the coordinates of two points on the line. In this case, use the two-point form of the line:
Just plug in the values from your two points, ( , ) and ( , ). It won't matter which point you designate 1 and which is called 2, so long as you are consistent after you have made the decision.
The reason that the two-point form works is because you are actually calculating the slope of the line with the  part. Compare the two-point form to the point-slope form: 
Hope this helps,
John
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