Slopes of Lines Slopes of Lines Chapter 3-3 Chapter 3-3
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Slopes of LinesSlopes of Lines
Chapter 3-3Chapter 3-3
Finding Slope of a LineFinding Slope of a Line
12
12
xx
yym
x in Change
y in Changem
Run
Risem
Remember! “Read” the line from left to right.
If it is going up, the slope is positiveIf it is going down, the slope is
negativeHorizontal lines have a slope of 0.
Equation is y={y-intercept}Vertical lines have “no slope” or
“undefined”Equation is x={x-intercept}
-8
2
Rise
Run
Find the Slope of a Line
42
8
run
rise)( Slope m
Lesson 3-3 Example 1
B. Find the slope of the line.Find the Slope of a Line
Use the slope formula.
Let (0, 4) be (x1, y1) and (0, –3) be (x2, y2).
which is undefined.
Answer: undefined
) ,( 11 yx
) ,( 22 yx
Lesson 3-3 Example 1
C. Find the slope of the line.
Find the Slope of a Line
Answer: ) ,( 11 yx
) ,( 22 yx
Lesson 3-3 Example 1
D. Find the slope of the line.
Find the Slope of a Line
Answer: 0
Lesson 3-3 CYP 1a
A. A
B. B
C. C
D. D
A. Find the slope of the line.
Lesson 3-3 CYP 1b
A. A
B. B
C. C
D. D
B. Find the slope of the line.
0
undefined
7
Lesson 3-3 CYP 1c
A. A
B. B
C. C
D. D
C. Find the slope of the line.
–2
2
Lesson 3-3 CYP 1d
A. A
B. B
C. C
D. D
D. Find the slope of the line.
0
undefined
3
Slopes of // and lines// lines have equal slope
ex: y = 2x + 4 // y = 2x – 6
Lines have opposite reciprocal slopes
ex: y = 5x – 3 y = x – 851
Lesson 3-3 Example 3
Determine Line Relationships
Find the slopes of and .
A. Determine whether and are parallel, perpendicular, or neither.
F(1, –3), G(–2, –1), H(5, 0), J(6, 3)
Neither
Lesson 3-3 Example 3
Determine Line Relationships
B. Determine whether and are parallel, perpendicular, or neither.
F(4, 2), G(6, –3), H(–1, 5), J(–3, 10)
Answer:
The slopes are the same, so and are parallel.
Lesson 3-3 CYP 3a
• The slopes are opposite reciprocals so they are
A.Find the slope of &Determine whether they are parallel, perpendicular, or neither.
A(–2, –1), B(4, 5), C(6, 1), D(9, –2)
24
15ABm 1
6
6
69
12CDm 1
3
3
Lesson 3-3 CYP 3a
• Neither
B. Find the slope of &Determine whether they are parallel, perpendicular, or neither.
A(7, –3), B(1, –2), C(4, 0), D(–3, 1)
71
32ABm
6
1
6
1
43
01CDm
7
1
7
1
Lesson 3-3 Example 4
Use Slope to Graph a Line
First find the slope of .
Graph the line that contains Q(5, 1) and is parallel to with M(–2, 4) and N(2, 1).
Slope formula
Substitution
Simplify.
Lesson 3-3 Example 4
Use Slope to Graph a Line
The slope of the line parallel to through Q(5, 1) is .
The slopes of two parallel lines are the same.
Graph the line.
Draw .
Start at (5, 1).
Move down 3 units.
Then move right 4 units.
Label the point R.
Answer:
Graph the line that contains Q(5, 1) and is parallel to with M(–2, 4) and N(2, 1).
1. A
2. B
3. C
4. D
Lesson 3-3 CYP 4
Graph the line that contains R(2, –1) and is parallel to with O(1, 6) and P(–3, 1).
A. B. C.
D. none of these
Homework:Homework:
pg 160: # 1,2, 6 – 20, 24 – 36 even, 48pg 160: # 1,2, 6 – 20, 24 – 36 even, 48
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