Linear Functions and Cost Analysis

This video tutorial covers linear functions, focusing on the relationship between dependent and independent variables. It explains how to represent these relationships graphically and through equations. The lesson includes an exit card exercise using a cell phone plan example to illustrate linear relationships. Students learn to write equations in words and symbols and calculate costs based on usage.

What is the general form of a linear function?

• y = mx + b

• y = a/x

• y = ax^2 + bx + c

• y = log(x)

In a linear function, what does the slope represent?

• The fixed cost

• The rate of change

• The maximum value

• The minimum value

What is a dependent variable in statistics?

• A variable that does not change

• A constant value

• A variable that is used to make predictions

• A variable that is predicted

What is the fixed monthly fee in the cell phone rate plan problem?

• $10

• $15

• $20

• $25

How is the total monthly cost related to the number of minutes used?

• Total cost is the fixed cost minus the cost per minute times the number of minutes

• Total cost is the fixed cost plus the cost per minute times the number of minutes

• Total cost is the fixed cost divided by the number of minutes

• Total cost is the fixed cost multiplied by the number of minutes

What is the equation in symbols for the total monthly cost y in terms of minutes x?

• y = 0.05x + 20

• y = 0.05 - 20x

• y = 20x + 0.05

• y = 20 - 0.05x

What is the y-intercept in the equation y = 0.05x + 20?

• x

• 20

• 0.05

• y

If 182 minutes are used, what is the total monthly cost?

• $29.10

• $28.10

• $30.10

• $27.10

What does the slope of 0.05 represent in the context of the cell phone plan?

• The fixed monthly fee

• The cost per minute

• The number of minutes used

• The total monthly cost

How would you express the total cost for 200 minutes in words?

• The total cost is $20 plus 5 cents times 200

• The total cost is $20 divided by 5 cents times 200

• The total cost is $20 times 5 cents times 200

• The total cost is $20 minus 5 cents times 200