This is an applet that generates two lines. One in blue that you can control by changing parameters m (slope) and b (yintercept). The second line is the red one and it is generated randomly. As an exercise, you need to find an equation to the red line of the slope intercept form:
y = mx + b
where m is the slope and b is the yintercept.
We suggest that you first use an analytical method to find the equation of the line and then use the applet to change m and b to solve the same question graphically. Finally compare the two results. This exercise helps you in problem solving and also to gain deep undertanding of the concepts of slope and yintercept.
TUTORIAL
1  click on the button above "click here to start" and MAXIMIZE the window obtained.
2  Use any analytical method to find an equation of the slope intercept form
y = mx + b
to the red line.
You first need to find two points on the graph of the line and then use the method in example 5 below.
3  Use the sliders to change m and b (top left) so that the two graphs are the same. Read the values of m and b and compare these values to those found analytically above.
4  Generate another question by clicking on the button "new line" (bottom left) . You can generate as many questions as you wish.
5  Example: A line passes through the points (1,2) and (0,5). Find an equation to this line of the form y = mx + b.
6  Solution to the example in 5.
First find the slope m = (5  2) / (0  1) = 3
The equation can be written as y = 3x + b. b can be found using the fact that one of the two points (1,2) , for example, is on the graph of the line
2 = 3(1) + b
and solve for b: b = 5.
The equation of the line can be written as y = 3x + 5.
You can check that the second point (0,5) is on the graph of the line:
5 = 3(0) + 5.
More References and links on lines and slopes.
