Chapter 5
5.1: Understanding Direct Proportion
Objective…
Part A: Identify Direct Proportion from a Table
Key Vocabulary…
Proportion
Direct
Proportion
Constant of
Proportionality
•
At a supermarket, each pound of strawberries costs $2. The table shows
the cost, y dollars, for x pound of strawberries.
o
An equation that says ________ ratios are equivalent is called a
________________________.
o
Determine a general rule from the table: _______________
o
Write two equivalent equations derived from the general rule:
o
State the constant of proportionality: __________________
Chapter 5
5.1: Understanding Direct Proportion
•
•
•
A pet storeowner uses a table to decide how many of a certain type of fish
to put in an aquarium. Tell whether the number of fish, f, is directly
proportional to the volume of the water, g gallons. If so,
o
Determine the general rule from the table: _______________
o
Write two equivalent equations derived from the general rule
o
State the constant of proportionality: __________________
The table shows the distance traveled by a snail, d centimeters, after t
hours. Tell whether d is directly proportional to t. If so,
o
Determine the general rule from the table: _______________
o
Write two equivalent equations derived from the general rule
o
State the constant of proportionality: __________________
The table shows the distance traveled by a school bus, y miles, after x
hours.
o
Determine the general rule from the table: _______________
o
Write two equivalent equations derived from the general rule
o
State the constant of proportionality: __________________
Chapter 5
5.1: Understanding Direct Proportion
•
The table shows the number of pitches made, y, in x innings of a baseball
game.
o
Determine the general rule from the table: _______________
o
Write two equivalent equations derived from the general rule
o
State the constant of proportionality: __________________
Part B: Identify Direct Proportion from an Equation
When y is __________________________________ to x, you can write
_______________. You can use algebra to write another form of this
equation, giving y in terms of x.
For example: _______________________
Practice… State whether each equation represents a direct proportion. If
so, identify the constant of proportionality.
1)
2)
1
y = 3x
2
y − 2 = 5x
3)
0.4y = x
4)
x = 1 − 2y
Chapter 5
5.1: Understanding Direct Proportion
Part C: Recognize that a Constant of Proportionality can be a Unit Rate
1) The table shows the price, P dollars, for x cans of soup. P is directly
proportional to x.
o Find the constant of proportionality: ____________________
o Write a direct proportion equation: _____________________
2) The table shows the number of baseballs, y, made in x days. The
number of baseballs made is directly proportional to the number of
days of production.
o Find the constant of proportionality: ____________________
o Write a direct proportion equation: _____________________
3) Alina is buying some baseball caps. Each cap costs $8. The amount
Alina pays for the caps id directly proportional to the number of caps
she buys.
o Write a direct proportion equation: _____________________
4) A café sells sandwiches for $4 each. The amount Jason pays for some
sandwiches is directly proportional to the number he buys.
o Write a direct proportion equation: _____________________
Chapter 5
5.1: Understanding Direct Proportion
Use: y
= kx
5) Y is directly proportional to x, and y – 3 when x = 9. Find the constant
of proportionality. Then write a direct proportion equation.
6) Q is directly proportional to p, and p = 12 when q = 24. Find the
constant of proportionality. Then write a direct proportion equation.
7) W is directly proportional to h, and w = 18 when h = 3. Find the
constant of proportionality. Then write a direct proportion equation.