Aim: Slopes of Parallel Lines Course: Applied Geometry

Do Now:

a. y = 2x + 5

b. y = 2x – 1

c. y = 2x + 2

Aim: What is the relationship between slopes of parallel lines?

What is the slope of each line?

2

2

2

Aim: Slopes of Parallel Lines Course: Applied Geometry

Slopes of Parallel Lines

Graph Equations a), b), and d) on the graphing calculator by

1. Clicking the Y = button and inputting

Y1 = 2x + 5

Y2 = 2x – 1

Y3 = 2x + 2

2. Click the Graph key and watch the graphs appear. Hit the Trace key and skip from line to line. Lines having equal slopes are parallel.

Lines having different slopes are not parallel.

Aim: Slopes of Parallel Lines Course: Applied Geometry

Points A(-4, 2), B (1, 2), C(1, -3) and D(-4, -3) form a quadrilateral.

a. Graph the points and draw quadrilateral ABCD

b. What are the slopes of sides AB, BC, CD and AD?

c. What kind of quadrilateral is ABCD? Explain

Model Problem

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

y

1 2 3 4 5 6 7 8 9-1-2-3-4-5-6

1

2

3

4

5

6

7

8

9

-1

-2

-3

-4

-5

-6

-7

-8

-9

B(1, 2)(-4, 2)A

C(1, -3)(-4, -3)D

5 units

5 units4 equal sides

4 right angles

SQUARE

Slope of AB = 0

Slope of CD = 0

Slope of AD = undefined

Slope of BC = undefined

Recall: Two lines are parallel if their slopes are equal and if the slopes of two lines are equal, the lines are parallel. AB || CD & AD || BC

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Quadrilateral ABCD has vertices A(0,-1), B(0,1), C(3,4), and D(3,2). Using coordinate geometry, determine what type of quadrilateral ABCD is.

A

B

C(3,4)

(0,1)

(0,-1)

(3,2)D

Just showing the graph is not enough - prove using the formula for slope.

13

3

03

14

BCslope

13

3

03

12

ADslope

UndefinedABslope

00

11

.0

2

33

24UndCDslope

Since the slope of BC and AD are the same, the lines are parallel.

Since the slope of AB and CD are the same, the lines are parallel.

BC || AD, AB || CD, ABCD is a parallelogram.

x

y

xx

yymslope

12

12

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = 2x – 2 and that has a y-intercept of 4

What is the equation of this new line?

(0, 4)

(1, 6)

(0, -2)

y =

2x -

2

y = 2x + 4

m = 2

m = 2 b = 4

y = mx + b

b = -2

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = 1/2x – 4 and that passes through point (2, 2)

What is the equation of this new line?

m = 1/2

y = 1/2x – 4

y = 1/2x + 1

y = mx + b

m = 1/2 b = 1

(4, 3)(2, 2)

(0, -4)

b = -4(0, 1)

Aim: Slopes of Parallel Lines Course: Applied Geometry

On Sketchpad:

Graph a line that is parallel to the line y = -1/4x + 3 and that passes through (3, 0).

Sketchpad:

GraphPlot New Function y = -1/4x + 3Enter

GraphPlot Points (3, 0)Plot

Plot a second point that would result in a line parallelto y = -1/4x + 3

Highlight new line Measure Slope and a 2nd timefor Equation.

On your calculator, sent the new equation Y1=

Model Problem

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = 2x + 1 and that passes through (0, -2).

6

4

2

-2

-4

-6

-5 5

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = -4x – 5 and that passes through (0, 2).

6

4

2

-2

-4

-6

-5 5

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = -4 and that passes through (0, -6).

6

4

2

-2

-4

-6

-5 5

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line y = 1/3x – 6 and that passes through (1, 2).

6

4

2

-2

-4

-6

-5 5

Aim: Slopes of Parallel Lines Course: Applied Geometry

Model Problem

Graph a line that is parallel to the line 2y = 4x – 6 and that passes through (-2, -4).

6

4

2

-2

-4

-6

-5 5