Slope of a line given: two points, graph and equation

1. SLOPE OF
A LINE

2. SLOPE
• Can be used to describe the steepness
of a line.

3. SLOPE
• Slope is sometimes referred to as the
“rate of change” between 2 points.

4. SLOPE
• The letter “m” is used to represent
slope. (m means modulus)

5. Slope can be expressed
different ways:
2 1
2 1
( ) vertical change
( ) horizontal change
y y rise
m
x x run

  


6. Slope
Slope may also be known
given an equation of a line.
A line whose equation is in
the form y = mx+b, m is
the slope.

7. Determining Slope (given two points)
• If the coordinates of two points on a
line are (𝑋1, 𝑌1) and (𝑋2, 𝑌2) the slope m
can be found as follows:
m =
𝑌2 − 𝑌1
𝑋2 − 𝑋1
, where 𝑋1 ≠ 𝑋2.
𝑌1 is read as “y sub 1”. The
number 1 is called subscript.

8. Determining Slope (given two points)
Find the slope of the line containing each
pair of points.
a. (-2, 1) and (4, 6)
𝑋1 , 𝑌1 𝑋2 , 𝑌2
m =
𝑌2 − 𝑌1
𝑋2 − 𝑋1
=
6 −1
4 −(−2)
=
5
6
It doesn’t matter which ordered
pair is selected as 𝑋1 , 𝑌1.

9. Determining Slope (given two points)
Find the slope of the line containing each
pair of points.
b. (-1, 5) and (2, 5)
𝑋1 , 𝑌1 𝑋2 , 𝑌2
m =
𝑌2 − 𝑌1
𝑋2 − 𝑋1
=
5 −5
2 −(−1)
=
0
3
= 0
It doesn’t matter which ordered
pair is selected as 𝑋1 , 𝑌1.

10. Determining Slope (using graph)
When given the graph, it is easier to
apply “rise over run”.
m =
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
m =
3
6
=
1
2v
3
6
v
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏

11. Types of Slope
Positive Negative Zero Undefined
or
No Slope

12. rise = 4
run = 5
m= rise
run
m= 4/5

13. Determining Slope (given equation)
A line whose equation is in the form
y = mx+b, m is the slope.
ex. A. 2x - 3y = 5
-3y = -2x + 5
y =
2
3
x -
5
3
Hence, m =
2
3

14. Determining Slope (given equation)
ex. B. 2x + y = 3
y = -2x + 3
Hence, m = -2