SLOPE
Intermediate 2 Math
Write down 3 observations about the bike ramps below
What characteristics can we find for each of the line segments?
Each line segment is the same length
The purple line segment is steeper than the red. It creates a sharper angle by going up 4 over 3 compared to the red which goes up 3 over 4.
3
4
4
3
When set up as fractions we see
Does is also work with other line segments?
Line segments are same length but
Orange line segment is less steep
Does is also work with an entire line that doesn’t have endpoints?
Lines are technically same length because they both stretch infinitely forever
the Blue line is steeper
by comparing points along the line we see that
Slope
a number that describes the direction and steepness of a straight line
denoted by the letter m
ratio is represented as a fraction (proper or improper, no mixed numbers)
slope =
change in y
change in x
rise
run
vertical change
horizontal change
Positive Slope:
Negative Slope:
the line is moving upward from Left to Right
the line is moving downward from Left to Right
=
=
Compare the line segments specified
line a & line b
both travel horizontally 8 units
vertically line a goes up 2 units
vertically line b goes up 1 unit
line a has a greater slope than line b
Compare the line segments specified
line a & line c
both travel horizontally 8 units
vertically line a goes up 2 units
vertically line c goes up 3 units
line c has a greater slope than line a
Compare the line segments specified
line c & line d
both travel vertically up 3 units
horizontally line c goes 8 units
horizontally line d goes 5 units
line d has a greater slope than line c
Compare the line segments specified
line c & line e
both travel vertically 3 units
both travel horizontally 8 units
Do these have the same slope?
each line has the same steepness,
but their directions are opposites
upward from
L to R
downward from
L to R
Find the slope of
− 6
1
m = −6
Find the slope of
2
5
Find the slope of
5
7
Find the slope of
− 1
6
Find the slope of
4
3
Find the slope of
− 4
4
What else do you notice about this line?
The slope between ANY two points on the
same straight line will always be equal
Find the slope of the treadmill
10 inches
48 inches
units cancel each other
slope does not need units, it is just a fraction
Pick 2 points on the line and find the slope
Find the slope between the points
What if there is no graph?
3
3
5
5
Slope Formula
a method of calculating the slope between two points
slope =
change in y
change in x
Find the slope between the points
What if the order of the co-ordinates was reversed?
As long as co-ordinates are paired above/below
the fraction bar the order does not matter
Find the slope between the points
What would be the slope if the y−coordinates were the same?
Horizontal lines have a slope of zero
What would be the slope if the x−coordinates were the same?
Vertical lines have a slope
that is undefined
Use the tables to find the slope of the line that contains the following points
− 6
− 6
+ 2
+ 2
+ 1
+ 2
− 7
− 14