1. CONSTANT OF PROPORTIONALITY!

2. WHAT IS IT? A constant ratio in any proportional relationship Really just another name for unit rate! Remember, to be constant means it never changes!

3. WITH RATIO TABLES Miles 50100150200 Gallons 2468 Find the unit rate! 25 miles per gallon This means our constant of proportionality is 25, so if we divide the miles by gallons we should always get 25. Let’s check! Find the constant of proportionality between the gallons and the miles.

4. TRY THIS ONE! Number of Apples 92736 Cost $3.00$9.00$12.00 Find the constant of proportionality between the gallons and the miles. Find the unit rate! Constant of proportionality = 3 Let’s Check!

5. WITH GRAPHS (0,0) (1,45) (2,90) (3,135) (4,180) 45 1 90 2 135 3 4 y x 180 Y 4590135180 X 1234 Find the constant of proportionality. To find our constant of proportionality we have to divide!

6. 45 1 = 90 2 =45 135 3 =45 180 4 =45 So, our constant of proportionality is 45. Y 4590135180 X 1234 Do you see that our x value multiplied by our constant of proportionality is our y value? We could write this like: y=45(x)

7. We will ALWAYS be able to write our constant of proportionality as an equation that looks like this: y=kx. Just like in our last example! y=45x. And k will always be our constant of proportionality!

8. WHAT CAN WE DO WITH IT? Population Density: Finding the constant of proportionality by dividing the population by the area. Finding how many per 1 square mile

9. POPULATION DENSITY Wildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in a 16 square mile area of the forest. In another part of the forest, conservationists counted 117 in a 13 square mile area. Then a third conservationist counted 216 deer in a 24 square mile area of the forest. Do the conservationists need to be worried? DeerSquare milesDo we have a constant of proportionality? 14416 11713 21624 YES!

10. POPULATION DENSITY So do the conservationists need to be worried? NOPE! The deer population is constant in the National Forest. Let’s write an equation! If we multiply our square miles by 9 we will have the number of deer. So our equation will look like: DeerSquare milesConstant of proportionality 144169 117139 216249 Deer = 9 x Miles OR y=9x