defining slope section 5.2 slope = = ________ is the ratio of vertical ______ to horizontal _____....
TRANSCRIPT
DEFINING SLOPESECTION 5.2
Slope = =
________ is the ratio of vertical ______ to horizontal _____.
Slope riserun
runrise
SLOPEMAN
My one weakness is
that I can only run to the right.
Ris
e
Run
If I run uphill, then the slope of the line
is positive.
Lines with a positive slope go
uphill from left to right.
Remember, I can only run to the
right!
Slopeman is going UPHILL so the slope is POSITIVE.
Lines with POSITIVE
slope go UP from left to
right
Ris
e
Run
If I run DOWNHILL, then the slope of the
line is NEGATIVE.
Lines with a NEGATIVE slope go
DOWN from left to right.
Remember, I can only run to the
right!
Slopeman is going
downhill so the slope is negative.
EXAMPLE 1: Find the slope of the following lines.
Ris
e
Ru n
riseslope =
run 2
2
Slope=m = 1
We use the
letter m to
represent slope.
EXAMPLE 1: Find the slope of the following lines.
31
riseslope =
run
31
Slope is
negative.
m = -3
EXAMPLE 1: Find the slope of the following lines.
riseslope =
run 1
21
2Slope is positive.
1
2m
Plot the following points on the graph and find the slope.
1
5
x y
4
6
4
2
Slope is positive.
42
2m
+ 4+ 2
difference in range
difference in domain + 4
+ 2
2
6
4
x y
9
1
-2-8
Example 2: Find the slope between the following points without graphing.
difference in range
difference in domain -2
-814
1
4m
3
-3
x y
-1
5
-6+ 6
Example 2: Find the slope between the following points without graphing.
difference in range
difference in domain -6
+6 1
1m
29
-52
x y
-31
14
-81
+45
Example 2: Find the slope between the following points without graphing.
difference in range
difference in domain -8
1+
45
95
9
5m
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.
21
21
xx
yy
2211 ,, yxandyxSlope = when the two points are
Example 3: Find the slope of the line containing the following points
9,6 and 1,4 6 4
9 128
14
1
4m
Example 3: Find the slope of the line containing the following points
1,3 and 5, 3
3 3
1 5 66
1
1m
Choose any two points on the line and find the slope of the line.
x y4 3
1 3
+0
-3
difference in range
difference in domain +
0-3 0m
The slope of any horizontal
line is zero.
If I tried to ski on this line, how fast
would I travel?
zero miles per hour
Choose any two points on the line and find the slope of the line.
x y-2 1
-2 -3
-4
+0
difference in range
difference in domain
-4+
0 m undefined
What would happen if I tried to ski off this vertical
cliff?
HELP !!
I would have UNDEFINED body parts!!
The slope of any vertical
line is undefined.