Name: _________________________________________
Date: _________________
Lesson 7-4: Constant Rate of Change and Direct
Variation
Key Vocabulary:

Linear Relationship – a relationship that has a _______________ graph
o Linear relationships have a constant rate of change.
Constant Rate of Change
Constant Rate of Change
Not a Constant Rate of Change

Direct Variation – a type of linear equation that describes a constant rate of change; this type of graph
always passes through the ____________.
o Equation: y = kx, where k is the constant of variation, also called the constant of
proportionality
Exercises:
1) As scuba divers descend below the surface of the ocean, the pressure they feel from water increases at a
constant rate. This is shown in the table below.
a. Find the constant rate of change for this function and interpret its
meaning.
b. Determine whether a proportional linear relationship exists between
the two quantities shown in the table.
c. Write an equation that relates the depth and the amount of water pressure.
2) Find a constant rate of change for the graph at the right.
3) Using the graph at the right, determine whether a proportional linear
relationships exists between the two quantities.
4) Using the graph at the right, write an equation that relates the number of shares and the total cost.
Find the constant rate of change for each linear function and interpret its meaning. Then, determine
whether a proportional linear relationship exists between the two quantities. If a proportional linear
relationship exists, write an equation relating the two quantities.
5)
6)
7)
8)
Unit 8 Summary
Rate of change =
A positive rate of change looks like:
A negative rate of change looks like:
To determine if a relationship is proportional, divide each of the ____-values by the ____-values, and see if the
ratios are _________. The graph of a proportional relationship goes through the _________, or (___,___).
If a proportional relationship exists, the constant ratio is called the _________ ___ ______________ in the
formula_______________. The constant ratio is the variable _____, and is equal to the ratio of _____ to _____.
The formula noted above is also called the ___________ _____________ equation.
A graph with a constant rate of change looks like:
A graph that does not have a constant rate of change looks like: