DEFINING SLOPE

1
DEFINING SLOPE
SECTION 5.2
2
Slope
rise
________ is the ratio of vertical ______ to
horizontal _____.
run
rise
Slope
run
My one weakness is that I can only run to the
right.
SLOPEMAN
3
Remember, I can only run to the right!
If I run uphill, then the slope of the line is
positive.
Lines with a positive slope go uphill from left
to right.
Rise
Run
4
Slopeman is going uphill so the slope is positive.
5
Remember, I can only run to the right!
If I run downhill, then the slope of the line is
negative.
Lines with a negative slope go downhill from left
to right.
Rise
Run
6
Slopeman is going downhill so the slope is
negative.
7
EXAMPLE 1 Find the slope of the following
lines.
2
2
Run
Rise
Slopem 1 We use the letter m to represent
slope.
8
EXAMPLE 1 Find the slope of the following
lines.
3
1
1
Slope is negative. m -3
3
9
EXAMPLE 1 Find the slope of the following
lines.
1
2
2
1
Slope is positive.
10
Plot the following points on the graph and find
the slope.
x
y
1 5
4 6
4
2
4
2
4
2
Slope is positive.
2
11
Example 2 Find the slope between the following
points without graphing.
x
y
6 4
9 1
-2
-8
-2
-8
12
Example 2 Find the slope between the following
points without graphing.
x
y
3 -3
-1 5
-6
6
-6
6
13
Example 2 Find the slope between the following
points without graphing.
x
y
29 -52
-31 14
-81
45
-81
45
14
Sometimes when you must find the slope of a line
without having a picture of the graph, it is
easier to find the slope of a line using the
following formula.
Slope
when the two points are
Example 3 Find the slope of the line
containing the following points
15
Example 3 Find the slope of the line
containing the following points
16
Choose any two points on the line and find the
slope of the line.
x
y
4 3
0
-3
1 3
0
-3
17
If I tried to ski on this line, how fast would I
travel?
zero miles per hour
The slope of any horizontal line is zero.
18
Choose any two points on the line and find the
slope of the line.
x
y
-2 1
-4
0
-2 -3
-4
0
19
What would happen if I tried to ski off this
vertical cliff?
20
HELP !!
21
Im falling and I cant get up!!
22
I would have UNDEFINED body parts!!
The slope of any vertical line is undefined.
23
Determining if lines will be parallel or
perpendicular
Parallel Lines When two lines are parallel,
their slopes are equal to each other
We can see that the two lines are parallel. We
prove it by determining that both lines have
equal slopes of
3
2
2
3
24
Determining if lines will be parallel or
perpendicular
Perpendicular Lines When two lines are
perpendicular, their slopes are opposite
reciprocals
We can see that the two lines are
perpendicular. We prove it by determining That
the lines have opposite, reciprocal slopes
3
3
2
2