# Traveling on 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.