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Constant of Proportionality!

Constant of Proportionality!. 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!. With ratio tables. Find the constant of proportionality between the gallons and the miles.

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Constant of Proportionality!

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

  4. Try this one! Find the constant of proportionality between the gallons and the miles. Let’s Check! Constant of proportionality = 3 Find the unit rate!

  5. With graphs Find the constant of proportionality. (4,180) (3,135) To find our constant of proportionality we have to divide! (2,90) (1,45) y (0,0) 45 90 135 180 3 2 4 x 1

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

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

  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? 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: Deer = 9 x Miles OR y=9x

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