Undefined Slope

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On an X-Y coordinate plane, when the points are written in the coordinate form of (x, y), then the slope of the line joining any two points can be found out since the slope of a line is the change in the y-coordinates to the change in the x-coordinates. This definition of slope is also popularly known as ‘rise over run’. Now, if change in the x-coordinates is ‘0’, then we get an undefined slope since the denominator goes to ‘0’.
 
Example 1: Calculate the slope of the line joining the points (3, 5) and (3, 9) in the X-Y coordinate plane.

Given two points: (3, 5) and (3, 9).

Slope of a line joining the two points (x1, y1) and (x2, y2) is given as:

Slope, m = (y2 – y1)/ (x2 – x1)

This gives: m = (9 – 5)/ (3 – 3) ==> m = 4/0

Now we get, ‘0’in the denominator and anything divided by ‘0’ is infinity.

Therefore we get an undefined slope and the line is a vertical line of equation x = 3.
 
Example 2: Calculate the slope of the line joining the points (-2, 4) and (-2, 7) in the X-Y coordinate plane.

Given two points: (-2, 4) and (-2, 7).

Slope of a line joining the two points (x1, y1) and (x2, y2) is given as:

Slope, m = (y2 – y1)/ (x2 – x1)

This gives: m = (7 - 4)/ (-2 – (-2)) ==> m = 3/0

Now we get, ‘0’ in the denominator and anything divided by ‘0’ is infinity.

Therefore the line has an undefined slope and the graph is a vertical line of equation x = -2.
 

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