Traveling on the Standard Line
- Author:
- Jaime Dianzon, agilitygordons
- Topic:
- Algebra, Linear Equations
Are you familiar with the standard line?
OBJECTIVE: To learn the standard form of the equation of a line
One of the most common forms of the equation of a line is the STANDARD FORM. While the starting form in deriving the equation of a line can vary depending on the given information, the final answer is usually written in STANDARD FORM: Ax + By = C.
Occasionally, you'll be asked to write the answer in the GENERAL FORM: Ax + By+ C = 0. So, all you have to do is transpose the constant term to the left side of the equation, leaving a zero on the right side.
Interact with the applet below to discover some facts about the STANDARD FORM.
INSTRUCTIONS:
1. Set slider b = 1.
2. Fix the position of point S and move the slider for point R.
3. Compute the ratio of C/A in the linear equation.
4. Now move point S to a new position and again move the slider for point R.
5. Compute the ratio of C/A in the linear equation.
6. Repeat Steps 2 and 3 for other positions of point S.
QUESTION: What do you notice about the ratio of C/A for each position of point S? How does the ratio relate to the position of point S in the graph.
INSTRUCTIONS:
1. Set slider b = 2.
2. Fix the position of point R and move the slider for point S.
3. Compute the ratio of C/B in the linear equation.
4. Now move point R to a new position and again move the slider for point S.
5. Compute the ratio of C/B in the linear equation.
6. Repeat Steps 2 and 3 for other positions of point R.
QUESTION: What do you notice about the ratio of C/B for each position of point R? How does the ratio relate to the position of point R in the graph.
QUESTION: What is the equation of the line when it coincides with the x-axis? when it coincides with the y-axis?
TODAY you learned about the standard form of the equation of a line and some of its properties.
In future lessons, you'll learn how to apply these properties to come up with the standard form of the equation of lines.