January 09, 2015
3-3 Proportional Relationships
Objective: To determine if relationships are
proportional
A proportional relationship is a relationship between inputs and
outputs in which the ratio of inputs and outputs is always the same.
-If the relationship is in a table, write the ratio of each input to its
corresponding output. If they are the same, then it is proportional!
Example:
Tomato Prices
2 pound for $3
4 pounds for $6
6 pounds for $9
January 09, 2015
Your turn ...
1. The ratios of all the inputs to the outputs in a table are 1/4. Is
this relationship proportional?
2. Pizza slices are selling as follows: 1 for $2, 2 for $3, and 4 for $5.
Is this relationship proportional? Explain.
Input-Output Tables and Graphs
Jenna earns $12 per hour making bracelets. She uses the function
e = 12h to track her earnings. e = earnings, and h = hours
Make an input-output table and graph your results. Does the function
have a proportional relationship? Explain.
Hours (h)
Earnings (e)
January 09, 2015
January 09, 2015
3-4 : Linear Functions
Objective: To recognize linear functions and use tables and equations to graph
A linear function is a function whose points lie on a straight line when the function
is graphed.
Ways to determine if a function is linear:
1. Use a table - if the ratios between the changes in the variables in a table
are the same, the function is linear
2. Make a graph - if the line is straight, the function is linear.
Example: Determine if the function represented by the table is linear.
1.
2.
x
1
2
3
4
x
2
1
-1
-4
y
6
8
10
14
y
-6
-3
3
12
January 09, 2015
Discrete data are data that involve a count of items, such as numbers of people or
cars. For discrete data, plot the data points and connect them with a dashed line.
Continuous data are data where numbers between any two data values have
meaning. Use a solid line to indicate continuous data.
Graphing Discrete Data
A gallon of milk costs $2.59. The total cost of g gallons of milk is a function of
the price of one gallon. Make a table and graph the function.
Gallons
$$
1
2
3
4
Graphing Continuous Data
Joe lifted weights and burned 100 calories. Then he walked and burned 257
calories per hour. The function c = 257h + 100 gives the total calories Joe burned
where c represents calories and h represents hours walking. Use the equation to
make a table and graph the function.
Time (h)
Calories