3.4 – find and use slopes. slope: measures the steepness of a line or the rate of change. slope =...
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3.4 – FIND AND USE SLOPES
Slope: measures the steepness of a line or the rate of change.
Slope = m = RiseRun
Up or downLeft or right
=
Type of Slope
Picture Numerical Value
Positive
Negative
Any Positive #
Any Negative #
Type of Slope
Picture Numerical Value
Zero
Undefined
0
Undefined
Horizontal line
Vertical line # .
0
1. Find the slope of the line through the given points.
P(3, -5) and Q(1, -1)
-4
2
Slope = =RiseRun
-4 2
= -2
1. Find the slope of the line through the given points.
4
8
Slope = =RiseRun
48
P(5, 2) and Q(-3, -2)
= 12
-6
Slope = =RiseRun
Undefined
1. Find the slope of the line through the given points.
P(-3, -3) and Q(-3, 3)
Slope Formula:
Slope = =RiseRun
For (x1, y1) and (x2, y2)
y2 – y1
x2 – x1
2. Find the slope of the line through the given points using the slope formula.
P(-2, -3) and Q(2, -5) (x1,y1) (x2,y2)
12
12
xx
yy
= –5 – (-3)2 – (-2)
= –24
1
2=
2. Find the slope of the line through the given points using the slope formula.
P(1, -1) and Q(-3, -9) (x1,y1) (x2,y2)
12
12
xx
yy
= –9 – (-1)–3 – 1
= –8–4
2=
2. Find the slope of the line through the given points using the slope formula.
P(3, -5) and Q(1, -5) (x1,y1) (x2,y2)
12
12
xx
yy
= –5 – (-5)1 – 3
= 0–2
0=
Name Definition Slope Relationship
Picture
Parallel lines
Intersecting lines
Lines that never intersect.
Same slope
Lines that cross at one point
ml
Not same
m = 2then m = 2
Perp. lines
Lines that cross forming right angles
Opposite AND reciprocal slopes
m = 2 becomes
m = – 12
ml
3. Decide whether the lines are parallel, perpendicular, or neither.
82
12
xy
xy2
15
xy
xy
53
2
113
2
xy
xy
34
5
75
4
xy
xy
neither perpendicular
parallel perpendicular
3. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer.
Line 1: (3, 1), (7, 2)Line 2: (-5, -3), (-1, -4)
12
12
xx
yy
2 1
7 3
1
4= =Line 1:
12
12
xx
yy
)5(1
)3(4
4
1= =Line 2:
neither
3. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer.
Line 1: (-9, 3), (-6, 7)Line 2: (-11, 5), (-7, 2)
12
12
xx
yy
7 3
6 ( 9)
4
3= =Line 1:
12
12
xx
yy
2 5
7 ( 11)
3
4
= =Line 2:
perpendicular