Open GeoGebra. Download GeoGebra or access the online applet from the Downloads¹ page at geogebra.org.classic².

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

1. Change to the Move Graphics View tool

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

We will be using the x-axis for the number of hours that Jill works and y-axis for the amount that she is paid in dollars. Plotting some points will help us construct the graph.

If Jill works for 6 hours she is paid $90. In other words, when x=6, y=90. In the input box, at the top left of the screen, type ‘(6,90)’ and press Enter. A point should appear at those coordinates.

How much is Jill paid if she works for zero hours? In the input box type (0,0) and press Enter.

Change to the Line through two points tool and click on the two points. This line graph represents the relationship between the number of hours Jill works and how much she is paid.

Use your graph to solve the problem. I.e. determine how much Jill is paid if she works for 10 hours by reading your graph.

• How does this compare to the amount she would be paid if she worked for 5 hours?

• What is the gradient of the graph?

• What is Jill’s hourly rate?

• What is the constant of proportionality between the amount Jill is paid and the number of hours she works?

Dynamic geometry, such as GeoGebra, is flexible and allows us to solve a range of problems easily.

Suppose we changed the problem:

The amount that Jill is paid is directly proportional to the hours she works. If she works for 4 hours she is paid $80. How much would she be paid if she worked for 10 hours?

We need to adjust the coordinates of A.

If Jill works for 4 hours she is paid $80. Type 'A=(4,80)' into the input box and press Enter.

Notice that the gradient of the graph changes. Use your graph to solve the new problem.

Suppose we adjust the problem again:

The amount that Jill is paid is directly proportional to the hours she works. If she works for 3 hours she is paid $57. How much would she be paid if she worked for 5 hours?

Use the input box to adjust the coordinates of A so that if Jill works for 3 hours she is paid $57.

Using the New Point tool, plot a point on the line graph.

Change to the Move tool, notice that you can slide the point along the graph.

Slide the point so that it’s x-coordinate is 5 then read its y-coordinate (to the nearest whole number) from the algebra window.

What is the solution to the problem?