The purpose of this applet is to investigate the [b]gradient-intercept form[/b] of a line, [b]y = mx + b[/b].[br]For an equation of a line to be in gradient-intercept form, [b]y[/b] must be the subject.[br]Note that [b]m[/b] is the coefficient of x and [b]b[/b] is the constant.[br]You can use the [b]sliders[/b] in the applet to change the values of [b]m[/b] and [b]b[/b].

[b]Tasks[/b][br][*] You can [b]drag the black slider[/b] to change the value of m (the coefficient of x).[br]1. Describe what happens to the line as m gets larger.[br]2. When m is [b]positive[/b] (m > 0) is the line [b]increasing or decreasing[/b] (from left to right)?[br]3. For what values of m is the line [b]decreasing[/b]?[br]4. You will notice that the value of b remains constant as you change the value of m. What feature of the graph also remains constant as m changes?[br]5. For what value of m is the line [b]horizontal[/b]? [br]6. What is the [b]equation[/b] of that horizontal line?[br][br][*] Click the reset button at the top right corner of the applet to return the sliders to their original positions. [color=#1551b5][b]Drag the blue slider[/b][/color] to change the value of b.[br]7. Describe what happens to the line as b increases.[br]8. What do you notice about the value of b and the point where the line cuts the y-axis?[br]8. You will notice that the value of m remains constant as you change b. What feature of the graph also remains constant as b changes?[br]9. For what value of b does the line pass through the [b]origin[/b]? [br]10. What is the [b]equation[/b] of that line?[br][br][*] In the gradient-intercept form of a line, [b]y = mx + b[/b][br]11. What property of the line does the value of m relate to?[br]12. What property of the line does the value of b relate to?[br][br][*] Click the check box to [color=#c51414][b]display a 2nd line[/b][/color]. This line shares the [b]same gradient[/b] (m value) as [color=#1551b5][b]Line1[/b][/color]. You can [color=#c51414][b]drag the red slider[/b][/color] to change the value of this line's constant, which is labelled as c.[br]13. What words could be used to describe the two lines?