# 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 = **m**x + 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) _________ __________ __________________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?