The Straight Line y = mx + c

This worksheet allows you to vary the gradient and y-intercept of a straight line. You will notice on the left hand window of the screen, that the line’s equation is displayed (in the ‘Dependent objects’ folder as object ‘a’). The coordinates of both points are also displayed in this section (in the ‘Free objects’ folder).

On the centre of the screen you will see that the line’s y-intercept value is displayed, as well as its gradient ‘m’. Notice that the gradient value is shown near a coloured triangle, which always has a value of 1 on the base and the gradient value on the vertical side. Remember that the gradient is always the rise over the run (in this case the run is always equal to 1).

Before you commence the questions at the bottom of the worksheet, familiarise yourself with how the interactive aspects of this worksheet operate.
1. Start by moving the point on the y-axis (it will only move up and down along the axis). As you move it, notice how the y-intercept value changes accordingly.
2. Then fix this point on the origin (0,0) and move the second point. This point can move anywhere on the plane. Notice, that as you move this point the gradient will change.

Now try the questions below the graph.

These questions are identical to those found in Activity 8.6 of your study book.

Use the interactive graph to determine the equation of a line with the following gradient and y-intercept:
1. m = 5, and c = -2
2. m = 3, and c = -1
3. m = 1, and c = 0
4. m = 0.5, and c = -5
5. m = -0.75 and c = 3.5

To do these, you will need to firstly move the first point so that the y-intercept is correct (remember the coordinates of this point are shown as A in the left hand window). Then move the second point so that the gradient is correct (it is displayed near the coloured triangle). Finally read off the equation of the line from the left hand window).

Colin Carmichael, 16/2/06, Created with GeoGebra