In The Slope of a Line, you learned that the slope, or m, of a line describes how rapidly or slowly change is occurring.
Negative Slope = Negative Correlation
A negative slope demonstrates a negative correlation between the following:
- x and y
- input and output
- independent variable and dependent variable
- cause and effect
Negative correlation occurs when the two variables of a function move in opposite directions. Look at the linear function in the picture. As the values of x increase, the values of y decrease. Moving from left to right, trace the line with your finger. Notice how the line decreases.
Next, moving from right to left, trace the line with your finger. As the values of x decrease, the values of y increase. Notice how the line increases.
Real World Examples of Negative Slope
Mr. Nguyen drinks caffeinated coffee two hours before his bed time. The more cups of coffee he drinks (input), the fewer hours he sleeps (output).
Aisha is purchasing a plane ticket. The fewer days between the purchase date and the departure date (input), the more money Aisha will spend on airfare (output).
Calculating Negative Slope
Refer to the PDF, Calculate.Negative.Slope to learn how to use a graph and the slope formula to calculate a negative slope. To download free software to view the PDF, visit http://get.adobe.com/reader/.