1. Finding The Slope Of A Line
A quick tutorial reviewing how to find slope of a line given two points

2. Definition of Slope
Slope is defined as the ratio of rise and run. It describes the rate at which a line rises or falls. Slope = m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛

3. Finding the Slope Begin by identifying ANY two points on the line
Slope = m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛
Begin by identifying ANY two points on the line
(8 , 10)
(2 , 6)

4. Find the Rise by subtracting the
Finding the Slope
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛
Find the Rise by subtracting the
y-values
(8 , 10)
(2 , 6)
Rise = 10 – 6 = 4

5. Find the Run by subtracting the
Finding the Slope
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛
Find the Run by subtracting the
x-values
(8 , 10)
(2 , 6)
Run = 8 – 2 = 6

6. write your answer as a fraction and be sure to reduce
Finding the Slope
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛 = = 2 3
write your answer as a fraction and be sure to reduce
(8 , 10)
(2 , 6)
m = 2 3

7. The Slope Formula
Slope = m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛
To make the formula, we begin by identifying two generic points
(x1 , y1) and (x2 , y2)
(x2 , y2)
(x1 , y1)

8. Again, Find the Rise by subtracting the y-values
The Slope Formula
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛
Again, Find the Rise by subtracting the y-values
(x2 , y2)
(x1 , y1)
Rise = y2 – y1

9. Again, Find the Run by subtracting the x-values
The Slope Formula
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛
Again, Find the Run by subtracting the x-values
(x2 , y2)
(x1 , y1)
Run = x2 – x1

10. The Slope Formula m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏
Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛 = 𝑦2 −𝑦1 𝑥2 −𝑥1
Again, write your answer as a fraction
(x2 , y2)
(x1 , y1)
m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏

11. Using The Slope Formula
(x1 , y1) = (3 , 10)
(x2 , y2) = (10 , 6)
(3 , 10)
(10 , 6)
m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏 = 𝟔 − 𝟏𝟎 𝟏𝟎 − 𝟑 = −𝟒 𝟕

12. WHAT IF….we choose the points in opposite order?
(x1 , y1) = (10 , 6)
(x2 , y2) = (3 , 10)
(3 , 10)
(10 , 6)
m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏 = 𝟏𝟎 − 𝟔 𝟑 −𝟏𝟎 = 𝟒 −𝟕 = −𝟒 𝟕
The order doesn’t matter, the sign remains the same in the end

13. A Final Example m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏 = −𝟏−𝟓 𝟔−(−𝟐) = −𝟔 𝟖 = −𝟑 𝟒
(x1 , y1) = (-2 , 5)
(x2 , y2) = (6 , -1)
(-2 , 5)
(6 , -1)
m = 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏 = −𝟏−𝟓 𝟔−(−𝟐) = −𝟔 𝟖 = −𝟑 𝟒