1. Do Now 2/8/12
In your notebook, answer the following question. There are two skateboard ramps at a skate park. One ramp is 12 ft long and 6 ft tall. The other is 10 ft long and 8 ft tall. Which ramp do you think is steeper? How can you tell?

2. Objective
SWBAT find the slope of a line and interpret slope as a rate of change

3. Section 8.4 “The Slope of a Line”
the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on a line.
Slope = rise = change in y
run change in x

4. Slope Symbols The slope m of a line passing through two points
and is the ratio of the rise change to the run. y
run
rise
“positive slope” x

5. Slope Symbols The slope m of a line passing through two points
and is the ratio of the rise change to the run. y
rise
run x
“negative slope”

6. Find a positive slope Find the slope of the line shown.
Let (x1, y1) = (–4, 2) = (x2, y2) = (2, 6).
m =
y2 – y1
x2 – x1
Write formula for slope.
6 – 2
2 – (– 4) =
Substitute. = 4 6 2 3
Simplify.

7. Find the slope of the line that passes through the points.
(5, 2) and (4, –1)
Let (x1, y1) = (5, 2) = (x2, y2) = (4, – 1).
m =
y2 – y1
x2 – x1
Write formula for slope.
(– 1) – 2
4 – 5 =
Substitute. =
– 3 –1
= 3
Simplify.

8. Find a negative slope XAMPLE 2 Find the slope of the line shown.
Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1).
m =
y2 – y1
x2 – x1
Write formula for slope.
–1 – 5
6 – 3 =
Substitute.
– 6 3 = –2
Simplify.

9. Find the slope of the line that passes through the points
(0, 6) and (5, –4)
Let (x1, y1) = (0, 6) and (x2, y2) = (5, – 4).
m =
y2 – y1
x2 – x1
Write formula for slope.
– 4 – 6
5 – 0 =
Substitute. 10 5
= – =
– 2
Simplify.

10. Find the slope of a horizontal and vertical line
Find the slope of the line shown.
Let (x1, y1) = (– 2, 4) and (x2, y2) = (4, 4).
m =
y2 – y1
x2 – x1
Write formula for slope.
4 – 4
4 – (– 2) =
Substitute. 6 =
Simplify.
EXAMPLE 4
Find the slope of the line shown.
Let (x1, y1) = (3, 5) and (x2, y2) = (3, 1).
m =
y2 – y1
x2 – x1
Write formula for slope.
1 – 5
3 – 3 =
Substitute.
– 4 =
Division by zero is undefined.

11. Identifying Slopes y2 – y1 m = x2 – x1 Positive slope Undefined
Slope of 0
Negative slope

12. Section 8.4 “Investigating Slope”
With a partner, complete the concept activity “Investigating Slope” on page 403 in your textbook.