Example: Find the general form of the circle

Solution:

Example: Find the general form of the circle

Solution:

**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?

**Example:** Find the equation of a line in slope intercept form given the slope of the line is and the line passes through the point

**Solution:**

Use the point-slope formula of the line to start building the line. m represents the slope of the line and is a point on the line.

**Point-slope formula:**

and

Substitute the values into the formula.

Since the instructions ask to write the equation in slope intercept form we will simplify and write the equation with y by itself on one side. I will also use the clearing fractions method to avoid having to add fractions.

(Multiply by LCM)

(Cancel Denominator)

The equation of a line in slope intercept form with a slope of and passing through the point is

**Example:** Find the equation of a line in slope intercept form given the line passes through the two points and .

**Solution:**

First find the slope of the line.

Choose one of the points to be and choose the other point to be .

I will choose to be and choose to be .

Substitute these values into the slope formula and simplify.

The slope of the line containing the points and is .

Then, use the point-slope formula of the line to start building the line. m represents the slope of the line and you can use or as the point on the line.

**Point-slope formula:**

and

Substitute the values into the formula.

Since the instructions ask to write the equation in slope intercept form we will simplify and write the equation with y by itself on one side.

The equation of a line in slope intercept form passing through the two points and is .

**Example:** Find the equation of a line in slope intercept form given the slope of the line is 7 and the line passes through the point

**Solution:**

Use the point-slope formula of the line to start building the line. m represents the slope of the line and is a point on the line.

**Point-slope formula:**

and

Substitute the values into the formula.

Since the instructions ask to write the equation in slope intercept form we will simplify and write the equation with y by itself on one side.

The equation of a line in slope intercept form with a slope of 7 and passing through the point is .

Example: Find the equation of the line.