PERPENDICULAR LINES

Linear Equations

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?

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.

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 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

STEPS TO WRITE EQUATION A LINE PERPENDICULAR TO A NON-VERTICAL, NON-HORIZONTAL LINE PASSING THROUGH A GIVEN POINT.

E X A M P LE : F IN D T H E E Q U AT IO N O F T H E L IN E P E R P E N D I CU L A R T O Y = T H AT PA S S E S T H R O U G H T H E P O IN T ( 3 , 0 )

1. Find the slope of the given line. The slope of your new line will be the opposite reciprocal of this.

2. Determine x and y from the given point.

3. Substitute m, x and y into the equation y=mx+b and solve for b.

4. Substitute your m and b into y=mx+b

Given m= , New m=-

x=3 and y=0

0=-(3)+b

0=-6+b

6=b

y=-2x+6

STEPS TO WRITE THE EQUATION OF THE LINE PARALLEL TO A VERTICAL

LINEEXAMPLE: FIND THE EQUATION OF A LINE PARALLEL TO X=5 THAT PASSES THROUGH (2, 1)

1. Determine the y-coordinate of the point

2. Write the equation of the line as y=_____

The y-coordinate is 1

y=1 is the equation of the line

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)

1. Determine the x-coordinate of the given point

2. Write the equation of the line as x=______

The x-coordinate is 2

The equation of the line is x=2