Formula for Slope m

The formula for the slope m of a line passing through two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

Case 1: m > 0 (Positive Slope)

Points: (x₁=1, y₁=1) and (x₂=2, y₂=2)

m = (2 – 1) / (2 – 1) = 1

The line rises as you move from left to right.

Case 2: m = 0 (Zero Slope)

Points: (x₁=1, y₁=1) and (x₂=2, y₂=1)

m = (1 – 1) / (2 – 1) = 0

The line is horizontal.

Case 3: m is Undefined (Vertical Line)

Points: (x₁=1, y₁=1) and (x₂=1, y₂=2)

m = (2 – 1) / (1 – 1) is undefined

The line is vertical.

Case 4: m < 0 (Negative Slope)

Points: (x₁=1, y₁=2) and (x₂=2, y₂=1)

m = (1 – 2) / (2 – 1) = -1

The line falls as you move from left to right.