Riding the Berms
- Author:
- Jaime Dianzon, Kevin Hopkins, Tim Brzezinski
How do you ride a berm fast?
OBJECTIVE: To learn how to graph a line on the Cartesian plane using the slope and the y-intercept
In a previous lesson, you were introduced to the STANDARD FORM of a line (Ax + By = C) and its relative, the GENERAL FORM (Ax + By + C = 0). When asked to find the equation of a line, you usually give your final answer in these forms.
Drawing the Line: https://www.geogebra.org/m/bb3cpjrn
In this lesson, you'll be introduced to another form of the equation of a line in which the final answer can be written—the SLOPE-INTERCEPT FORM (y = mx + b).
Interact with the applet below to discover some facts about the SLOPE-INTERCEPT FORM.
INSTRUCTIONS
1. Set slider m = 5 and slider b = 5.
2. Keep slider m = 5 and move slider b. Observe the movement of the graph.
3. Keep slider b = 5 and move slider m. Observe the movement of the graph.
4. Try other combinations of m and b. Observe how the graph behaves.
QUESTION: What happens to the graph when you move slider b while keeping slider m fixed?
QUESTION: What happens to the graph when you move slider m while keeping slider b fixed?
QUESTION: What do m and b represent in the formula: y = mx + b.
INSTRUCTIONS
Use the applet below to complete the following table. Click "Show Hint" for the values of rise and run. The first has been done for you.
Points Rise/Run Where Line Crosses Y-Axis Equation
A (0, -1), (7, 4) ___5/7___ ___(0, -1)__ ____
____
B (0, -4), (6, 3) _________ __________ ________________
C (5, 1), (0, 4) _________ __________ ________________
D (-4, -1), (0, -3) _________ __________ ________________
E (0, 4), (2, 0) _________ __________ ________________
F (0, 3), (8, 3) _________ __________ ________________
G (-5, 5), (0, -1) _________ __________ ________________
H (0, 0), (2, 2) _________ __________ ________________
I (0, 7), (-2, 5) _________ __________ ________________
J (-3, -4), (0, -6) _________ __________ ________________
____
B (0, -4), (6, 3) _________ __________ ________________
C (5, 1), (0, 4) _________ __________ ________________
D (-4, -1), (0, -3) _________ __________ ________________
E (0, 4), (2, 0) _________ __________ ________________
F (0, 3), (8, 3) _________ __________ ________________
G (-5, 5), (0, -1) _________ __________ ________________
H (0, 0), (2, 2) _________ __________ ________________
I (0, 7), (-2, 5) _________ __________ ________________
J (-3, -4), (0, -6) _________ __________ ________________
QUESTION: For each row, do you notice any relationship among the values of rise/run, the point where the line crosses the y-axis, and the equation of the line? Briefly explain.
Interact with the applet below to practice graphing lines using the slope and the y-intercept.
If your graph is correct, a big "Correct!!!" sign will appear. Otherwise, you'll have to try again.
Repeat as many times as needed to master the concept.
TODAY you were introduced to the SLOPE-INTERCEPT FORM of the equation of a line.
You discovered some of its properties, and you learned how to use the slope and the y-intercept to graph the line on the Cartesian plane. In future lessons, you'll discover more interesting facts about lines. Did you ENJOY your experience?