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.