Parallel and Perpendicular Lines in the Cartesian Plane

Parallel and Perpendicular Lines in the

Cartesian Plane

They are boring!

They have no use in life.

STEREOTYPES ABOUT PARALLEL AND PERPENDICULAR LINES

Just a series of lines with positive slopes…

No Big Deal

Color coded to show

parallel and

perpendicular lines

WHOA!

I know… I’m Awesome!

PARALLEL AND PERPENDICULAR LINES ARE EVERYWHERE

Construction

Maps

Sports

Artwork

y = mx + b m is the slope of the lineb is the y-intercept

REVIEW: SLOPE INTERCEPT FORM

Life is easy when you’re

in slope

intercept form

y = mx + bThe y-intercept is the y value when x = 0.

Visually, the y-intercept is y value when the line crosses the y axis

http://www.mathsisfun.com/data/function-grapher.php

Y -INTERCEPT

my = mx + bSlope Slider

Slope ofvertical lines?

SLOPE(𝑥1 , 𝑦1)

(𝑥2 , 𝑦 2)

3y = 6x + 95y = 10xy = -1x = 3

IDENTIFYING THE SLOPE AND THE Y-INTERCEPT

Hint

y = mx + bGiven the slope, m, and a point, (x , y), then we can find b, the y-intercept.

b = y – mxOnce we find b, we can find the equation of the line.

REVIEW: FINDING THE EQUATION OF THE LINE GIVEN A SLOPE AND A POINT ON THE LINE

p = (-2 , 2) m = 4

p = (-3 , 4) m = -2

p = (-2 , 2/3) m = -4/3

PRACTICE: FINDING THE EQUATION OF THE LINE GIVEN THE SLOPE AND A POINT ON THE LINE

1. Graph line segments. Be sure that each endpoint is an integer coordinate, such as (1,3) or (-3,0)Compute and record their slope.

2. Then graph a parallel line to each of the three line segments. Compute and record the slopes of the parallel lines. Then delete the parallel lines.

3. Then graph a perpendicular line to each of the three line segments. Compute and record the slopes of the perpendicular lines.

GRAPHING ACTIVITY

PARALLEL LINESTwo lines

are parallel

The lines never

intersect

Slopes are

equal

y = (1/3)x + 2 y – 1 = 6x2y = 5x + 34y = 8xy = 6x = -3

FIND THE SLOPE OF A PARALLEL LINE

PERPENDICULAR LINESTwo lines

are perpendicul

ar

The lines intersect at right angle

Slopes are negative reciprocal

s

y = -3x – 2y = (1/3)x + 2 y – 1 = 6x2y = 5x + 3y = 6x = -3

FIND THE SLOPE OF A PERPENDICULAR LINE

y = (1/3)x + 2 , p = (2 , -3)

2y = 5x + 3 , p = (1/2 , 2/3)

y = 6 , p = (6 , 0)

x = -3 , p = (1 , 2)

FIND THE EQUATION OF THE PARALLEL LINE THAT PASSES THROUGH THE GIVEN POINT.

y = -3x – 2 , p = (-1 , 4)

4y = 8x , p = (1 , 1/3)

y = 6 , p = (6 , 0)

x = -3 , p = (1 , 2)

FIND THE EQUATION OF THE PERPENDICULAR LINE THAT PASSES

THROUGH THE GIVEN POINT.