Slope!
The steepness of a line is called _____________!
Circle the line with the biggest slope…
The letter we use for slope is a lowercase ____! Why?! Because it comes from the French word monter which
means to climb or to rise. FUN FACT!
When given the graph of a line, we need to know a simple definition of slope:
m=
** Slope is the ratio of a line’s ___________________ change to its __________________________ change.
That’s what we mean by “rise over run”!
How to find slope when given the graph of a line:
1) Mark some points on the line.
2) Start from the ______________
3) Find the “rise” (or “fall”)
𝑚=
Up is ____________________
Down is ____________________
4) Find the “run” (we will always “run” right)
Later in the lesson we will be using a formula to find slope. We will often get fractions that need to be reduced.
The images below show four attempts at finding the slope of the line above. Can they all be correct…?
1
2
2
4
→
3
6
→
4
8
→
© Eddie McCarthy, 2017. Graphs made with Desmos
Let’s find the slope of the following lines!
𝑚=
𝑚=
𝑚=
𝑚=
𝑚=
𝑚=
There are four types of slopes…
As we travel left to right,
the graph goes _______.
As we travel left to right,
the graph goes _______.
Type of slope:
Type of slope:
__________________
__________________
This graph is not steep
at all!
This graph is so steep we
can't even call it a slope!
Type of slope:
Type of slope:
__________________
__________________
© Eddie McCarthy, 2017. Graphs made with Desmos
Sometimes we are not given a graph, but instead we are given 2 points on the line. When this is the case, we
must implement another definition of slope.
The slope of the line containing two points (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) can be found using the formula below:
Or in other words…
𝑚=
𝑚=
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛
Let’s find the slope of the line containing the points (−4, 1) and (2, 3).
The images below explain what we just did…
2
2 − (−4) = 6
3−1=2
6
→
1
3
Before we start finding slopes, let’s practice rewriting some “weird” fractions…
−3
9
4
−7
4
=
=
=
10
1
−8
=
4
=
1
0
12
=
−7
1
0
−2
=
=
−2
=
−3
12
0
=
−1
−8
=
−2
0
=
Let’s find the slope of the lines containing the following points.
(4, −1) & (6, 2)
(3, −2) & (4, 3)
(0, 4) & (−3, 12)
(−1, 7) & (−3, 1)
(3, 7) & (−11, 7)
(−5, 4) & (−5, 10)
© Eddie McCarthy, 2017. Graphs made with Desmos