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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. The slope is the coefficient of x. That means the number in front of x. 1 2. 1 2. -2. 4. 2 3. -2 3. Homework. -5 & 10 6 & -8.5 16 & -8 -5.3 & 4 - PowerPoint PPT Presentation
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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!