Example: Find the general form of the circle

Solution:

Example: Find the general form of the circle

Solution:

**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

**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

**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.

**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**

**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)

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?

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.

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?