Jack is employed as a salesperson for ElectroCorp. His job is to try to sign households up to ElectroCorp as their electricity supplier. He receives $50 for each household that he signs up.

Copy and complete this table to show how much money Jack earns.

What is the constant of proportionality between the amount of money Jack earns (y) and the number of households that he signs up (x)?

Write an equation to show the relationship between these variables.

Suppose that Jack’s commission increased to $60. What would the new equation of the graph be?

We can use a graph in GeoGebra to model Jack’s situation.

1. Open GeoGebra.
   Download GeoGebra or access the applet online from the Download¹ page at www.geogebra.org/classic².

2. We are going to use a slider so that we can adjust Jack’s commission:

   1. Click on the Slider tool.

   2. Click on the grid (perhaps near the top left corner of the grid).

   3. A window appears.

      1. Type ‘commission’ for the name of the slider.

      2. Type ‘0’ for the 'min' value.

      3. Type ‘100’ for the 'max' value.

      4. Type ‘10’ for the increment.

      5. Click Ok.

3. In the input box at the top left of the screen type ‘y=commission*x’. (We use the asterisk for multiplication.)

Use the Move tool to slide the slider. As you change the value of the commission, what feature of the graph changes?

Adjust the scale on the y-axis to see more of the graph:

1. Change to the Move Graphics View tool.

2. Click and drag downwards on the y-axis anywhere above the origin until you can see 200 on the y-axis.

Change back to the Move tool so that you can slide the slider.

Predict the answer for each of the questions below. Check your answer by using the graph.

1. If Jack’s commission is $10 per household, how much will he earn if signs up five households?

2. If Jack’s commission is $20 per household, how much would be earn if signs up five households?

3. If Jack’s commission is $50 per household, how much would be earn if signs up four households?

4. If Jack’s commission is $70 per sign-up, how much would be earn if signs up two households?