# 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?

# Finding the Equation of a line given a fractional slope and a point

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

# Finding the Equation of a Line given two points on the line

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  .

# Finding the Equation of a Line given the slope and a point

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.

# X-intercepts and Y-intercepts

An x-intercept is where the graph touches or crosses the x-axis.

A y-intercept is where the graph touches of crosses the y-axis.

In this picture, the graph crosses the x-axis at the ordered pair .  Since every ordered pair on the x-axis has a y coordinate of zero we can let to find x-intercepts.

To find an x-intercept: Let y=0 and solve for x.

In this picture, the graph crosses the y-axis at the ordered pair .  Since every ordered pair on the y-axis has a x coordinate of zero we can let to find y-intercepts.

To find an y-intercept: Let x=0 and solve for y.