Bell Ringer

Bell Ringer What is the slope of the following

equations?

a. y = x + 9

b. y = -2x – 8

c. y = 7 + 4x

d. y = 5 – x

12

23

12

-2

4

-2 3

The slope is the coefficient of x. That means the number in

front of x.

Homework

1. 122. -123. 114. 35. 116. 167. 3 & -78. 7 & -2.3

9. -5 & 1010. 6 & -8.511. 16 & -812. -5.3 & 413. 11 & -

1114. 9 & -1915. -6 & 6

News…

All late work due tomorrow for 3rd quarter report cards.

We will begin a new unit today! Yeah!No school Friday! Yeah!Report card pick up – April 19th

PSAE April 24th & 25th

Only 11th graders will be in school!

That means no school for you!YEAH!

Parallel and Perpendicular Lines

GRE 604: Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a pointPPF 301: Exhibit some knowledge of the angles associated with parallel linesPPF 401: Find the measure of an angle using properties of parallel linesPPF 402: Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°)PPF 501: Use several angle properties to find an unknown angle

Parallel Lines

Lines in the same plane that do not intersect are called parallel lines.

Parallel lines have the same slope.

These two lines are parallel. They

will never intersect!

Parallel Lines

You can also identify parallel lines by their equations!

y = 3x + 7y = 3x – 9

These two lines are parallel. Their slopes are the same!

(Notice that they have different y-intercepts!)

Parallel Lines

Which of the following equations are parallel?

A. y = 5x + 7 B. y = 2x – 8 C. y = -2x + 1

D. y = 2x – 9 E. y = 5 + 4x F. y = -9 + 6x

G. y = 6x – 7 H. y = 8 – 2x I. y = 5x – 1

J. y = -3x + 1 K. y = 7 + 4x L. y = -3x

Perpendicular Lines Lines that intersect at right angles (900)

are perpendicular. Perpendicular lines have slopes that are

negative reciprocals. The product of their slopes = -1.

These two lines are perpendicular. They

intersect at a right angle.

Perpendicular Lines

Negative reciprocals

1. What is the reciprocal of ?

2. What is the reciprocal of 3?

23

32

So the negative reciprocal is – ! 32

13

So the negative reciprocal is – ! 13

Perpendicular Lines

These equations are perpendicular:

y = 2x + 8

y = - x – 5

y = - x – 7

y = x + 5

12

45

32

54

2 • - ½ = -1The products of their

slope equal -1!

- 4/5 • 5/4 = -1The products of their

slope equal -1!

Perpendicular Lines

Are these equations perpendicular?

A. y = 4x + 7 B. y = - x – 8

y = - x + 9 y = x – 5

C. y = 3x – 2 D. y = 2 + 5x

y = x – 8 y = - x + 3

E. y = 8x – 7 F. y = 8 – 2x

y = 7 + x y = 2 + x

14

23

32

13

12

18

12

Yes! Yes!

Yes!

Yes!

No!

No!