Slope Calculator

Step 1: Identify Two Distinct Points

Select points P1(x₁, y₁) and P2(x₂, y₂) on the line to be analyzed.

Why: Slope is defined as the ratio of vertical to horizontal change between two points.

Step 2: Ensure Points Are Different

Verify that (x₁, y₁) ≠ (x₂, y₂); if they're identical, no unique slope exists.

Why: Different points are required for the denominator (x₂ - x₁) to be non-zero.

Step 3: Calculate Vertical Change (Rise)

Subtract: rise = y₂ - y₁ (change in y-coordinate).

Why: Rise measures how far the line goes up or down between the points.

Step 4: Calculate Horizontal Change (Run)

Subtract: run = x₂ - x₁ (change in x-coordinate).

Why: Run measures the horizontal distance; combining with rise yields the slope ratio.

Step 5: Divide to Find Slope; Convert to Angle

m = rise / run; then θ = arctan(m) to get the angle of inclination.

Why: Slope as a decimal is useful algebraically; angle provides geometric intuition.