Describe two different ways you could determine whether a function is linear. Describe how these two methods relate to one another, and a possible classroom activity that would help students to see this connection
What will be an ideal response?
There are a variety of possible methods. A few include the following:
• Graphing the data points of the function to see whether they form a straight line
• Examining a table of the data sets and looking at whether the increase from each x and y value to the next is proportional
Example: The ratio of the change in the x to that of y is always 2/5.
• Examining the function in equation form; if it is a first-degree equation (independent and dependent variables have only an understood exponent of 1), it is linear.
There are a number of different ways to show how these methods are related and classroom activities that could be used to illustrate. Those that would be most effective should be in a context. One possible example could involve helping students see the connection between the table and the graph of a linear function. For instance, students could use the situation at the top of the text page 283, which describes Brian's hotdog cart. They could create a table of values for hotdogs sold
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What will be an ideal response?