Graphing the Slope Lecture

Hello class, I am Professor Abdulla.
Today I will be teaching you all how to graph the slope of a function in a fun and easy way.

Also referred to as rise over run, you must refer to the graph as positive, negative, zero, or undefined. Follow this story about Sam to learn how and why linear graphs are the way they are.

The following is a mountain, a desert, and a cliff. Sam decided to go on a hiking trip and is walking up the mountain.

There are two important rules to remember about the way Sam goes.
1. Sam can only travel from left to right.
2. The only item Sam has with him is a parachute.

While Sam is traveling up the mountain, does he have a positive or negative rise?
The answer is positive, because he is traveling UP the mountain.
Does he have a positive or negative run?
Also positive, because he is traveling to the left.

So once you have the rise and the run, put them in the equation used to find slope: rise over run. Since both are positive and a positive divided by a positive is a positive, that means the slope is positive.

While Sam is traveling down the mountain, does he have a positive or negative rise?
The answer is positive, because he is traveling DOWN the mountain.
Does he have a positive or negative run?
Positive, because he is still traveling to the left.
Note that the steepness of the mountain does not change the 'negative' property of the line, and the slope is now negative.

As he travels east he crosses the desert, hot and thirsty.

His rise is zero because he is going neither up nor down, and he run is positive because he is still going left. Therefore the slope is zero because zero divided by a positive number is still zero. 

Sam approaches the edge of the cliff and uses the parachute to go straight up. Therefore the rise is positive and the run is zero. This makes the slope undefined because a number divided by zero makes it undefined. 

Now you can figure out how to graph a slope using the rise over run, and figure out if they are positive, negative, zero or undefined by figuring out if it is going up or down the mountain, going across the desert or up the cliff!