# 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?

# Calculating Slope

Given two points on the line and , you can calculate the slope of a line by the following formula.

is also know as  or “the change in y.”

is also know as  or “the change in x.”

Example: Calculate the slope of the line containing the points and .

Solution: 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 .

Example: Calculate the slope of the line containing the points and .

Solution: 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 .

Example: Finding the slope with the formula.

Example: Finding the slope with the formula.

Example: Finding the slope from the graph.

# Interpretation of slope

The slope of a line is a number that indicates the “steepness” of a line.  Slope is usually denoted with the letter m.

If the slope of the line is positive, the line will be rising or increasing from left to right.

All three of the above graphs have a positive slope and the line is rising or increasing from left to right.  Notice as the value of the slope gets larger, the line is getting steeper.

If the slope of the line is negative, the line will be falling or decreasing from left to right.

All three of the above graphs have a negative slope and the line is falling or decreasing from left to right.  Notice as the value of the slope gets smaller, the line is getting steeper.

If the slope is zero, the line will be constant.  This results in a horizontal line.

All three of the the above graphs have a slope of zero.  The y values are constant.

A vertical line has a slope that is undefined.

All three of the vertical lines have undefined slope.