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

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

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)

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

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

write your answer as a fraction and be sure to reduce Finding the Slope Slope = m = 𝑹𝒊𝒔𝒆 𝑅𝑢𝑛 = 4 6 = 2 3 write your answer as a fraction and be sure to reduce (8 , 10) (2 , 6) m = 2 3

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)

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

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

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

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

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

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