The Slope “Rate of Change”

The Rate of Change Slope = 0 No rate of change Rise = 0, Run = (whatever) Flat Surface Yawn!! Zzzz... No (zero) Slope = No Rate of Change

I might want to move… Small Slope = Slow Rate of Change Slope = 1/3 Small rate of change Rise = 1, Run = 3 Slight Downhill

Slope = 5 Bigger rate of change Rise = 10, Run = 2 Steep Downhill YIKES!! RUN!! HA HA! Large Slope = Fast Rate of Change

Infinite (∞) Slope = No Rate of Change The Slope never touches the ball, so it has no affect on the ball. No affect means no rate of change. It’s called “Undefined” Looks like a cliff

Recap No (Zero) Slope = No Rate of Change Small Slope = Slow Rate of Change Large Slope = Fast Rate of Change Infinite (∞) Slope = “Undefined” (No Effect) Slope = 0Slope = ⅓Slope = 5Slope = ∞ No ChangeSmaller ChangeBigger ChangeUndefined Change Flat SurfaceSlight Downhill (or Uphill) Steep Downhill (or Uphill) A Cliff Rise = 0 = Flat Surface Usually when Rise < Run Usually when Rise > Run Run = 0 = Cliff

Uphill or Downhill? Positive Slopes are UPHILL Negative Slopes are DOWNHILL

Slope Describe the next few slope values as: a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d)Cliff, ∞ slope, Undefined Change

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Small Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Click on the Correct Answer)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Rise = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Rise > Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b)Slight Up/Downhill, Small Slopes Smaller Change c)Steep Up/Downhill, Large Slopes Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Run = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Notice how Rise < Run)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Click on the Correct Answer)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Rise = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b)Slight Up/Downhill, Small Slopes Smaller Change c)Steep Up/Downhill, Large Slopes Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Run = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is Rise < Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Notice how Rise > Run)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Click on the Correct Answer)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Rise > Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b)Slight Up/Downhill, Small Slopes Smaller Change c)Steep Up/Downhill, Large Slopes Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Run = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is Rise < Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Notice how Rise = 0)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Click on the Correct Answer)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is the Rise > Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is Rise < Run?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b) Slight Up/Downhill, Small Slopes, Smaller Change c) Steep Up/Downhill, Large Slopes, Bigger Change d) Cliff, ∞ slope, Undefined Change (Is Rise = 0?)

Questions (Part I) a) Flat Surface, Zero Slope, No Change b)Slight Up/Downhill, Small Slopes Smaller Change c)Steep Up/Downhill, Large Slopes Bigger Change d) Cliff, ∞ slope, Undefined Change (Notice how the Run = 0)

Questions (Part II) Identify each of the following slope values as either: a)Going Uphill(U) Or b) Going Downhill(D)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill Is the slope positive or negative? (click on “doh” to try again) U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D Is the slope positive or negative? (Click on “doh” to try again) 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D Is the slope positive or negative? (Click on “doh” to try again) 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D Is the slope positive or negative? (Click on “doh” to try again) 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D Is the slope positive or negative? (Click on “doh” to try again) 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D Is the slope positive or negative? (Click on “doh” to try again) 1) 2) 3) 4) 5) 6)

Select (U)phill or (D)ownhill U D U D U D U D U D U D 1) 2) 3) 4) 5) 6)

In Conclusion Bigger Numbers = Steeper Slopes (Bigger Change) Zero Slope = Flat Line (No Change) Infinite Slope = Cliff (Undefined Change) Positive Slope = Uphill Negative Slope = Downhill

Homework