Equations of proportional
relationships
What we’ve learned…..
• Proportional relationships have a
constant ratio, or unit rate.
• The constant ratio, or unit rate, can also
be called the constant of
proportionality.
• The graph of a proportional relationship
is a straight line that passes through the
origin.
New vocabulary…..
• A proportional relationship can be
called a direct variation.
• Proportions can be represented by the
equation
y = kx
where k is the constant of
proportionality.
Writing an equation from the graph
of a proportional relationship
Ex. 1) The number of students that can go on a trip is
proportional to the number of chaperones that are available.
(4, 24)
(3, 18)
(2, 12)
A) Find the constant of proportionality k,
or the unit rate, of this relationship.
students
chaperones
6
1
12 6

2 1
k
6 students
1 chaperone
18 6

3 1
24 6

4
1
(1, 6)
B) Write an equation to represent this
relationship.
y = kx
No. of students
No. of chaperones
y = 6x
Writing an equation from a table of values
Ex. 2) In Mrs. McCarthy’s new car, the number of miles driven is
proportional to the gallons of gas used.
A) Find the constant of proportionality k,
or the unit rate, of this relationship.
y
miles
30 miles

k
x gallons
1 gallon
B) Write an equation to
represent this relationship.
y = kx
No. of miles
180 30

6
1
240 30

8
1
300 30

10
1
360 30

12
1
y = 30x
Gallons of
gas used
Writing an equation from a verbal statement
Ex. 3) If y varies directly with x, write the equation for this
relationship 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.
C) What is the value of y when x=7?
k
y
x
k
6
3
2
y = kx
y = 3x
y = 3x
y = 3(7)
y = 21 when x = 7
Writing an equation from a verbal statement
Ex. 4) It costs $5 to send 6 packages through a certain shipping
company. Consider the number of packages per dollar.
A) Find the constant of proportionality k,
or the unit rate, for this situation.
k
y packages

x
dollars
k
6
 1.2
5
B) Write an equation to represent
this relationship.
Number of packages y = k(dollars x)
y = 1.2x