​What is slope?

• Slope measures the steepness of a line.

  • The bigger the slope, the steeper the line.

  • The smaller the slope, the flatter it gets. ​

• Slope also tells us the direction of the line - if it goes up, down, or if it's horizontal or vertical.

• There are 4 different types of slope, depending on the direction of the line.

Suppose you were adding $100 to your bank account each week (that's a positive change!).  As time goes by, the amount of money you have in the account is increasing.  If you graphed this situation, the line would go up to the right to show that the amount of money is increasing as time goes by.

​

Positive Slope

Suppose instead of putting money into your bank account, you're spending $100 each week (this is a negative change!).  If you graphed this, the line would go down to the right to show that the amount of money you have in your account is decreasing.

​

Negative Slope

For example, if you just left your bank account alone and didn't put money in or take money out (and no interest was added).  This is an example of a situation with a rate of change equal to zero, nothing is happening! To show that there is 0 amount of change, the graph would be a flat horizontal line. This shows that the amount of money isn't changing.

​

Zero Slope

Think about the bank account example.  It wouldn't make sense if the graph was a vertical line. That would you mean you had all sorts of different amounts in the bank at the same exact moment, which isn't possible.

​

Undefined Slope

​Slope is calculated as the ratio of the amount of vertical change to horizontal change.  The easiest way to remember this is that slope is equal to "Rise over Run."

​When calculating slope: