Investigating gradient-intercept form of a line
- Author:
- Greg Chung
The purpose of this applet is to investigate the gradient-intercept form of a line, y = mx + b.
For an equation of a line to be in gradient-intercept form, y must be the subject.
Note that m is the coefficient of x and b is the constant.
You can use the sliders in the applet to change the values of m and b.
Tasks
You can drag the black slider to change the value of m (the coefficient of x).
1. Describe what happens to the line as m gets larger.
2. When m is positive (m > 0) is the line increasing or decreasing (from left to right)?
3. For what values of m is the line decreasing?
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?
5. For what value of m is the line horizontal?
6. What is the equation of that horizontal line?
Click the reset button at the top right corner of the applet to return the sliders to their original positions. Drag the blue slider to change the value of b.
7. Describe what happens to the line as b increases.
8. What do you notice about the value of b and the point where the line cuts the y-axis?
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?
9. For what value of b does the line pass through the origin?
10. What is the equation of that line?
In the gradient-intercept form of a line, y = mx + b
11. What property of the line does the value of m relate to?
12. What property of the line does the value of b relate to?
Click the check box to display a 2nd line. This line shares the same gradient (m value) as Line1. You can drag the red slider to change the value of this line's constant, which is labelled as c.
13. What words could be used to describe the two lines?