1. Representing proportional relationships with equations through COP or Constant of Proportionality

2. Old Thoughts……
Proportional relationships have a constant ratio, or unit rate.
The graph of a proportional relationship is a straight line that passes through the origin.

3. where k is the constant of proportionality or COP.
New vocabulary…..
The constant ratio, or unit rate, can also be called the constant of proportionality.
Direct variations can be represented by the equation y = kx
where k is the constant of proportionality or COP.

4. Example #1
Ex. 1) The number of chaperones needed varies directly with the number of students going on a trip.
A) Find the constant of proportionality k, or the unit rate, of this relationship.
(4, 24)
(3, 18)
(2, 12)
(1, 6)
B) Write an equation to represent this relationship.
y = kx
No. of students
No. of chaperones
y = 6x

5. Example #2
Ex. 2) In Mr. Miller’s new car, the number of miles driven varies directly with the gallons of gas used.
A) Find the constant of proportionality k, or the unit rate, of this relationship.
B) Write an equation to represent this relationship.
y = kx
Gallons of gas used
No. of miles
y = 30x

6. Example #3
Ex. 3) If y varies directly with x, write the equation for the direct variation if y = 6 when x = 2.
A) Find the constant of proportionality k, or the unit rate, of this relationship.
B) Write an equation to represent this relationship.
y = kx
y = 3x
y = 3x
C) What is the value of y when x=7?
y = 3(7)
y = 21 when x = 7