SME
Grade 7 Math · Ratios & Proportions
Proportional relationships and the constant of proportionality
Use this for “y is proportional to x, and y = 10 when x = 4. What is the constant of proportionality?”
Chart
y = 2.5x
The line goes through (0, 0) and (1, 2.5).
x = 4
y = 10
k = 2.5
This is an example. Type your own values to start a new problem.
k
Constant of proportionality
example
x
Input
example
y
Output
calculated
Formulas
y
=
kx
(output
=
constant
of
proportionality
×
input)
10 = 2.5 × 4
Assumptions
•
In a proportional relationship, y ÷ x is the same number k for every pair: the constant of proportionality.
•
The graph is a straight line through (0, 0), and it passes through (1, k).
•
k is the unit rate: y for one x.
•
If any pair gives a different y ÷ x, the relationship is not proportional.
Step-by-step
WE KNOW
k = 2.5 (constant of proportionality), x = 4 (input)
FIND
output (y)
Step 1 · Find output (y)
Use y = kx (output = constant of proportionality × input)
Multiply the input by the constant of proportionality.
y
=
2.5
×
4
y
=
10
Check
Put the numbers back in. Both sides should match.
10 = 2.5 × 4 ✓
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