Proportional Relationships in Tables, Graphs, and Equations
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.
