A government may tax a good or service in order to generate revenue. This will result in smaller producer and consumer surpluses and in dead weight loss. The tax burden is carried by the producer and consumer and can be calculated using different areas on the supply-demand graph for the good or service.

Mathematical straight line functions are used to calculate the corresponding price(s), (the y-value), asked and/or paid for a given quantity of a product, (the x-value). Equations to calculate the areas of rectangles and triangles are used to calculate different areas on the supply-demand graph.

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1. Use structured practice to explain how to calculate the y-value in a simple equation as follows:

• Write a simple equation such as y = 2x + 4 on the board.
• Write the following steps on the board, explaining the method.
  • Step 1: substitute x with 3 in the equation. [y = 2(3) + 4]
  • Step 2: calculate the value of y. [y = 6 + 4 = 10]

[Answers may vary if a different equation and/or different values of x are used.]

1. Distribute a copy of Activity 1: Calculate Function Values to each student. Ask students to study the information on mapping in number 1.
2. Divide the students into pairs and ask them to use the given example to answer number 2a-2c on Activity 1. Review answers.
   1. The given “rule” comprises of how many numbers? [The rule or equation is comprised of two numbers represented by x and y.]
   2. How will you use the “rule” to calculate one number if another is given? [One of the numbers can be calculated by substituting a value for the other number in the equation and doing the necessary calculations.]
   3. Explain the meaning of “correspondence between two numbers” in your own words. [Correspondence between two numbers means that for every value of x (or y) a value for the other number y (or x) may be calculated.]
3. Use guided practice in number 3, Activity 1, to allow students to practice calculating the y-value of an equation. Ask students to consider the equation: 4x – 3 = y. Ask, “If x = 1, could the value of y possibly be 7?” [Y cannot be 7: y = 4 (1) – 3 = 4-3 = 1]
4. Ask students to calculate the value of y in each example and complete the table in number 4 of Activity 1. After students have had time to work, draw the table on the board and with student input, complete the table, explaining the process in all three cases. Allow each student to mark and/or correct his/her own answers.

x

y

4x – 3 = y

Possible questions and answers

1

0

-3

4(0) – 3 = 0-3 = – 3

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Why is 4(0) = 0?

Multiplying by 0 always give 0

2

-1

-7

4(-1) – 3 = -4 – 3 = -7

Why is 4(-1) = -4?

Multiplying a negative number by a positive number always gives a negative answer.

Why is -4-3 = -7?

Adding 2 negative numbers will always give a negative answer.

3

3

9

4(3) – 3 = 12 – 3 = 9

1. Ask students to study the examples in number 5a and 5b in Activity 1.
2. Allow students to practice calculating the y-value in 6a and 6b either individually or in pairs. Ask two students to do the calculations on the board while the rest of the class identifies possible mistakes or evaluates the answers.

a. f(x) = 2/3(x) – 4 if x = 9

= 2/3(9) – 4

= 6 -4

= 2

b. 3y – 8x = 10 if x = – 2

3y – 8( -2) = 10

3y + 16 = 10

3y = 10 -16

y = -6/3

= – 2

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