Slope
Slope is a number that describes how steep a
line is.
slope =
rise
vertical change
=
run
horizontal change
Course 3
Slope
The slope of a horizontal line is 0. The
slope of a vertical line is undefined.
There is no “rise” (y value),
because the line doesn’t go
up or down.
Remember!
When any number is divided by zero, the
quotient is undefined. There is no answer.
Course 3
Slope
Slopes of Parallel and Perpendicular Lines
Two lines with equal slopes are parallel.
Two lines whose slopes have a product of –1
are perpendicular.
Helpful Hint
If a line has slope a , then a line
b
b
perpendicular to it has slope – a .
Course 3
Slope
The slope of a line tells you how quickly one variable changes in relation
to the other variable.
Ex 1 : A staircase has risers that are 20 cm high and treads that are 24 cm
deep. Express the slope in simplest terms.
Rise= 24 cm
Slope= rise = 20= 5
run 24 6
Run= 20 cm
Course 3
Slope
Ex 2- Find the slope of the line.
How to Find Slope
Step 1 : Choose 2 points that are
on the line (-2,1) (4,4)
run
rise
Slope= rise = = 3 units
run
6 units
(4,4)
Step 2: Count the units of
change between the points-
(-2,1)
You can find the difference
between them mathematically
y2-y1
x2-x1
4-1
3
=
4-(-2)
6
Course 3
=
1
2
Ex 3: The band is having a car wash to raise money. They earn $3 for
each car that they wash.
y = 3x
y = Dollars raised
x = # of cars washed
Cars washed
(x)
1
2
3
4
5
6
Dollars Earned
(y)
3
6
9
12
15
18
These values can be written as ordered pairs
(1,3) (2,6)
(3,9)
(4,5)
(5,15)
(6,18)
To find the slope, choose two of the points & find the change in y
change in x
Slope =
6-3 = 3 = 3
2-1 1