# Circle: Find General Form from Standard Form

Example:  Find the general form of the circle

Solution:

# Using the Distance Formula

The Distance Formula

Suppose A is and B is

The distance between points A and B is given by the following formula.

Example: Find the y-coordinate of the points that are 5 units away from the point (3,3) that have an x-coordinate of -1.

or

or

# Finding the Distance

The Distance Formula

Suppose A is and B is

The distance between points A and B is given by the following formula.

Example: Find the distance between points A and B.

Point A is and point B is

# Finding the Midpoint

The Midpoint Formula

Suppose A is and B is

The midpoint of the line segment joining points A and B is given by the following formula.

Example: Find the midpoint of a line segment joining points A and B.

Point A is and point B is

The x coordinate of the midpoint can be found by averaging the x-values of point A and B.  The y-coordinate of the midpoint can be found by averaging the y-values of point A and B.

# Forms of Linear Equations

Slope Intercept Form

m is the slope of the line and is the y-intercept

Point Slope Form

m is the slope of the line and is a point on the line.

Standard Form of a Line

# Graphing Linear Equations with Slope Intercept Form

Example: Graph the linear equation using the slope and the y-intercept. (the slope is positive and fractional)

Example: Graph the linear equation using the slope and the y-intercept. (positive and negative fractional slopes)

Example: Graph the linear equation using the slope and the y-intercept. (equation written in standard form)

# Perpendicular Lines and Parallel Lines

Example: What are parallel and perpendicular lines?

Example: How are the slopes of parallel and perpendicular lines related? (only watch until 1 min 20 seconds)

Example: Are the lines parallel, perpendicular or neither?

Example: Are the lines perpendicular to each other?

# Finding the equation of a line perpendicular to another line

Example: Find the equation of a line perpendicular to another line and passing through a specific point. (The other line in slope intercept form)

Example: Find the equation of a line perpendicular to another line and passing through a specific point. (The other line in slope standard form)

Example: Find the equation of a line perpendicular to the x-axis.

Example: Find the equation of a line perpendicular to the x-axis and perpendicular to the y-axis.

# Finding the Equation of a Line parallel to another line

Example: Find the equation of the line parallel to another line and passing through a specific point. (parallel equation in slope intercept form)

Example: Find the equation of the line parallel to another line and passing though a specific point. (parallel line in standard form)

Example: Find the equation of the line parallel to the x-axis or y-axis and passing through a specific point.

Example: What is an equation parallel to the y-axis?

Example: What is an equation parallel to the x-axis?