This is an applet that generates two lines. One in blue that you can control by changing parameters m (slope) and b (y-intercept). 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 y-intercept.
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 y-intercept.
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.