Proportional Relationships in Tables, Graphs, and Equations

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A video rental box charges customers $1 per day.

1 (proportional)

Beverly earns $150 a week for 10 weeks

15 (proportional)

A jet ski rental charges tourists for $35 per hour.

35 (proportional)

Ratio

A comparison of two quantities

Unit Rate

A ratio between different measurements in which the second term is one

y = kx , where k is the constant of proportionality (also sometimes written as y=ax or y=mx)

An equation representing a proportional relationship must be in this form.

The graph must form a straight line AND the line must pass through the origin (0,0).

How can you tell if a graph represents a proportional relationship?

Find all the ratios of y/x. If all the ratios are equivalent, then it's a proportional relationship.

How can you tell if a table of (x, y) values represents a proportional relationship?

The COP = y/x

How do you find the constant of proportionality?

A rental company charges $80 per day and a one-time fee of $24

Non-proportional

Proportion

Two ratios that are equal

Proportional relationships have

a graph that goes through the origin.

Non-proportional relationships have

a graph that may be a non-linear function.

On a graph, proportional relationships look like.....

a linear function (straight line).

Non-proportional relationships are written

in y=mx+b (or y=ax+b or y=kx+b) form.

2/10 and 5/20

non-proportional

3/4 and 1/10

non-proportional

3/9 and 4/16

non-proportional

4/12 and 1/2

non-proportional

4/20 and 4/16

non-proportional

a straight line that does not pass through the point of origin in the graph

non-proportional

ratios are not equivalent

non-proportional

y=1/2x-3

non-proportional

y=6x+1

non-proportional

y=9x-2

non-proportional

1/11 and 3/33

proportional

1/2 and 4/8

proportional

1/3 and 2/6

proportional

1/5 and 3/15

proportional

3/4 and 6/8

proportional

a straight line that passes through the point of origin in the graph

proportional

ratios are equivalent

proportional

y=1/3x

proportional

y=12x

proportional

y=4x

proportional

In equation form, proportional relationships are written as....

y=mx or y=ax or y=kx form.


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