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Slope Calculator – Find Slope Between Two Points | Solvezi
Slope Calculator – Find Slope Between Two Points | Solvezi
ΔX = x₂ − x₁ = 5 − 1 = 4 ΔY = y₂ − y₁ = 10 − 2 = 8
m = ΔY / ΔX = 8 / 4 = 2 ≈ 2
Using y = mx + b and Point P₁(x₁, y₁): b = y₁ - mRaw*x₁ b = 2 - (2 × 1) = 0 ≈ 0
d = √[(ΔX)² + (ΔY)²] d = √[(4)² + (8)²] d = 8.94427191
Understand slope and line properties with formulas, practical applications, and mini examples. Input two points P₁(x₁, y₁) and P₂(x₂, y₂) to explore slope, distance, equations, and angles.
Slope measures the steepness and direction of a line. Positive slope → line rises, negative → falls.
Formula: m = (Y₂ − Y₁) / (X₂ − X₁)
Applications: Road gradients, roof slopes, economic trend lines, engineering design.
Example: P₁(2,3), P₂(5,9) → m = (9−3)/(5−2) = 6/3 = 2
Distance is the straight-line length between two points.
Formula: d = √((X₂ − X₁)² + (Y₂ − Y₁)²)
Applications: Physics (displacement), navigation, engineering, mapping.
Example: P₁(1,2), P₂(4,6) → d = √((4−1)² + (6−2)²) = √(9+16) = √25 = 5
Horizontal movement between points.
Formula: X₂ − X₁
Applications: Used in slope, gradients, mapping coordinates.
Example: P₁(2,5), P₂(6,9) → Run = 6−2 = 4
Vertical movement between points.
Formula: Y₂ − Y₁
Applications: Slope, elevation calculations, physics.
Example: P₁(2,5), P₂(6,9) → Rise = 9−5 = 4
Depending on known values, a line can be expressed in multiple forms. Each form has practical applications:
y = m × x + b
Used when slope and y-intercept are known. Example: y = 2x + 1
y − Y₁ = m × (x − X₁)
Use when a point on the line and slope are known. Example: y−3 = 2(x−1)
A × x + B × y = C
Used for algebraic analysis, finding intersections. Example: 2x − y = 1