1. Perpendicular Lines
Linear Equations

2. I can find the equation of a line parallel to a given line passing through a given point.
Essential Question: Do you use the x- or y-coordinate to find the equation parallel to x=8? How do you know?

3. Perpendicular lines are lines in the same plane that intersect to form a right angle.
The symbol for perpendicular lines is
Sketch two perpendicular lines. (Be sure to show they intersect to form a right angle by putting a box in the angle)
You can determine if two lines are perpendicular by comparing their slopes.

4. When will lines be perpendicular?
Non-vertical and non-horizontal lines have slopes that are opposite reciprocals. This means you change the sign and flip it. These lines can have the same y-intercepts, but do not need to.
Example: y=2x+3 is perpendicular to y=− 1 2 x+3
A line will be perpendicular to a vertical line if it is a horizontal line.
Example: x=5 is perpendicular to y=9
A line will be perpendicular to a horizontal line if it is vertical.
Example: y=0 is perpendicular to x=7

5. Steps to write equation a line perpendicular to a non-vertical, non-horizontal line passing through a given point. Example: find the equation of the line perpendicular to y= 1 2 𝑥+3 that passes through the point (3, 0)
Find the slope of the given line. The slope of your new line will be the opposite reciprocal of this.
Determine x and y from the given point.
Substitute m, x and y into the equation y=mx+b and solve for b.
Substitute your m and b into y=mx+b
Given m= , New m=- 2 1
x=3 and y=0
0=- 2 1 (3)+b
0=-6+b
6=b
y=-2x+6

6. y=1 is the equation of the line
Steps to write the equation of the line parallel to a vertical line example: find the equation of a line parallel to x=5 that passes through (2, 1)
Determine the y-coordinate of the point
Write the equation of the line as y=_____
The y-coordinate is 1
y=1 is the equation of the line

7. The equation of the line is x=2
Steps to find the equation of a line perpendicular to a horizontal line passing through a given point example: find the equation of a line perpendicular to y=7 that passes through the point (2,3)
Determine the x-coordinate of the given point
Write the equation of the line as x=______
The x-coordinate is 2
The equation of the line is x=2