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# Undefined Slope

## The Slope of a Vertical Line is Undefined

Undefined slope

Jennifer Ledwith

In The Slope of a Line, you learned that the slope, or m, of a line describes how rapidly or slowly change is occurring.

Linear Functions have 4 types of slopes: positive, negative, zero, and undefined.

### Real World Example of Undefined Slope

Refer to the graph, Undefined slope. The x-axis represents the number of movie tickets, in hundreds, that a theater sells. The y-axis represents the revenues, in thousands of dollars, that the movie theater will earn. When 200 movie tickets are sold, what are the theater’s revenues? You could answer any value from \$0 to \$2,000, and according to the graph, you’d be correct. Of course, this graph doesn’t make sense. Each input (number of movie tickets sold) can only have one output (revenues).

### The Slope of a Vertical Line is Undefined

Let’s look at the slope. Revenues increase by \$2,000, but the number of tickets sold remains the same. Remember, slope is rise/run. What is \$2,000/0? Anything divided by 0 is undefined.

### Calculating an Undefined Slope

Refer to the PDF, Calculate_Undefined_Slope, to learn how to use a graph and the slope formula to calculate an undefined slope. To download free software to view the PDF, visit http://get.adobe.com/reader/.

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