Slope-Intercept Form: m and b
- Straight Lines
Understanding how m and b change the graph of the equation.
The sliders can be changed to adjust the values of m and b. The values of m and b will directly affect the graph of the line. The equation of the line is also given in the box on the left. Answer the following questions on a piece of paper. 1. Write the equation of the line with m=1 and b=1? 2. What does the point B represent in this graph? 3. Move the slider for b. As you increase the value of b, how does the point B change on the graph? 4. As you decrease b, how does the point B change on the graph. 5. As you move the b-slider, does the slope of the graph change? 6. Move the b slider to the position b=0. What is the equation of the line? How is that different from your equation in question 1? 7. Reset your sliders to the original positions in question 1. Increase your m-slider. Does your graph become steeper or flatter? 8. Now decrease your m-slider until you reach m=0. Does your graph become steeper or flatter? 9. When m=0, describe the type of line you have? 10. Write the equation of that line from question 9. What happened to the x? Why does it not show up? 11. Now take the m-slider and decrease the value of m below zero. Does the line get steeper or flatter? 12. Now increase the m-slider until you reach m=0. Again, does the line get steeper or flatter? 13. As you have been moving the m-slider, has your point B moved at all? Why is that? 14. Look at when m=1 and m=-1. How do the 2 lines differ? When m=4 and m=-4? 15. When the m value is positive, does the graph graph go up or down as it goes from left to right? 16. When the m value is negative, does the graph graph go up or down as it goes from left to right? 17. Write a rule to help you remember the information from questions 15 and 16.