Proportional Relationships

Tables

100

Table shows: Proportional or not? What is the algebraic rule?

x     y

1     4

2     8

3     12

Proportional: y = 4x

200

Table shows: Is it proportional? How do you know?

x     y

0     3

1     7

2     11

Non-proportional: It does not pass through the origin (0,0)

300

Table shows: What is the constant of proportionality.

x     y

1     2

2     4

3     6

2

400

Table show: What is the algebraic rule

x     y

1     3

2     6

4     12

y = 3x

500

Table shows: Is it proportional? Explain why

x     y

0     0

1     2.5

2     5

yes, it has a constant and passes through the origin

Graphs

100

What two things must a proportional graph have?

Be a straight line (linear) and pass through the origin

200

True or False:

A line that is straight but starts at (0,5) is proportional 

False

300

If the constant of proportionality is 3, name one point on the graph besides (0,0)

examples: (1,3) (2,6) (3,9) (4,12)......

400

A graph shows points (1,4) and (2,8). Write an algebraic rule

y = 4x

500

Explain why y = 2x + 1 is not proportional by looking at its graph

the line does not pass through the origin

When you plug 0 in for x, you do not get 0 for y

Equations

100

Identify the constant of proportionality: y = 5x

5

200

is y = 7x + 2 proportional?

No, plus two means it is not going through the origin

300

Write an algebraic rule for a relationship where y is 1/2 of x

y = 0.5x

400

Solve: if y = 4x and y = 92, what is x

23

500

Create an algebraic rule for a line that goes through (0,0) and (3,18)

y = 6x

Vocabulary

100

the number you multiply x by to get y 

constant of proportionality or coefficient

200

a proportional relationship always starts at which ordered pair

origin (0,0)

300

True or false: all proportional relationships are linear

true

400

what is another name for constant of proportionality 

unit rate

500

give one real life example of a proportional relationship

cost of apples per pound

miles per hour

miles per gallon

Mixed

100

find the missing value if x = 3 and y = ? When y = 4x

12

200

explain why y = x + x is proportional or not.

yes, y = 2x, constant ratio is 2

300

a recipe uses 2 cups of sugar for 5 cups of flour. find the constant of proportionality (sugar per flour)

2/5 or 0.4

400

choose the proportional set: 

A) (0,0) (1,6) (2,14)

B) (0,0) (1,3) (2,6)

C) (0,0) (1,4) (2,6)

B

500

a line passes through (2,12) and (4,22). Write its equation and constant of proportionality

y = 5x + 2