What is SLOPE? Algebra I, Unit 4

What is SLOPE? If you have ever walked up or down a hill, then you have already experienced a real life example of slope. As you go up hill, you may feel like you are spending lots of energy to get yourself to move. The steeper the hill, the harder it is for you to keep yourself moving. Keeping this fact in mind, by definition, SLOPE is the measure of the steepness of a line.

How do we find slope?

Four types of SLOPE: In math, slope is defined from left to right. I repeat we always measure slope going from left to right. This is very important! There are four types of slope you can encounter. positive negative zero undefined

Positive SLOPE: Lines that have positive slope, slant “up hill” (as viewed from left to right). Ski Bird has to work hard to make it up the hill.  He needs to exert more positive (+) energy to get up the hill.

Example #1 Find the slope of the line containing (-4, 2) and (2, 6). +6 +4

Negative SLOPE: Lines that have negative slope, slant “down hill” (as viewed from left to right). Ski Bird enjoys the ride down the hill.  He needs to decrease (-) energy to try to slow down.

Example #2 Find the slope of the line containing (3, 5) and (6, -1). -6 +3

What if . . . we used different points on the same line, such as (4, 3) and (5, 1)? -2 +3

Zero SLOPE: Lines that are horizontal have zero slope. Ski Bird is cross- country skiing on level ground.  He is not working hard to get up a hill, nor is he trying to slow down.  His energy level (and his enjoyment level) is at zero.

Example #3 Find the slope of the line containing (-2, 4) and (4, 4). +6

Undefined SLOPE: Vertical lines have undefined slope. Ski Bird cannot ski vertically.  Sheer doom awaits Ski Bird at the bottom of a vertical hill.

Example #4 Find the slope of the line containing (3, 5) and (3, 1). -4