Slope-Intercept Form Calculator

Slope-Intercept Form is evaluated from Point 1 - x₁, Point 1 - y₁ and Point 2 - x₂. The calculation reports Slope, Y-Intercept and X-Intercept.

Results

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About the Slope-Intercept Form Calculator

Slope-Intercept Form is treated here as a quantitative relation between Point 1 - x₁, Point 1 - y₁, Point 2 - x₂ and Point 2 - y₂ and Slope, Y-Intercept, X-Intercept and Equation.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Slope = rise/run = (y₂ - y₁)/(x₂ - x₁). Y-intercept: plug slope and one point into y = mx + b, solve for b.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Slope = rise/run = (y₂ - y₁)/(x₂ - x₁). Y-intercept: plug slope and one point into y = mx + b, solve for b.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Points (1, 3) and (4, 9)

Inputs

x1: 1 y1: 3 x2: 4 y2: 9
Slope: 2. Y-Intercept: 1. X-Intercept: -0.5. Equation: y = 2x + 1. Distance Between Points: 6.7082

With Point 1 - x₁ = 1, Point 1 - y₁ = 3, Point 2 - x₂ = 4 and Point 2 - y₂ = 9 as the stated inputs, the result is Slope = 2, Y-Intercept = 1 and X-Intercept = -0.5. Each value corresponds to the declared output fields.

Example 2: Points (-2, 5) and (3, -5) — negative slope

Inputs

x1: -2 y1: 5 x2: 3 y2: -5
Slope: -2. Y-Intercept: 1. X-Intercept: 0.5. Equation: y = -2x + 1. Distance Between Points: 11.1803

With Point 1 - x₁ = -2, Point 1 - y₁ = 5, Point 2 - x₂ = 3 and Point 2 - y₂ = -5 as the stated inputs, the result is Slope = -2, Y-Intercept = 1 and X-Intercept = 0.5. Each value corresponds to the declared output fields.

Example 3: Points (0, -4) and (6, 0) — x and y intercepts given

Inputs

x1: 0 y1: -4 x2: 6 y2: 0
Slope: 0.6667. Y-Intercept: -4. X-Intercept: 6. Equation: y = 0.6667x - 4. Distance Between Points: 7.2111

With Point 1 - x₁ = 0, Point 1 - y₁ = -4, Point 2 - x₂ = 6 and Point 2 - y₂ = 0 as the stated inputs, the result is Slope = 0.6667, Y-Intercept = -4 and X-Intercept = 6. Each value corresponds to the declared output fields.

Example 4: Points (2, 2) and (5, 2) — horizontal line

Inputs

x1: 2 y1: 2 x2: 5 y2: 2
Slope: 0. Y-Intercept: 2. X-Intercept: inf. Equation: y = 0x + 2. Distance Between Points: 3

With Point 1 - x₁ = 2, Point 1 - y₁ = 2, Point 2 - x₂ = 5 and Point 2 - y₂ = 2 as the stated inputs, the result is Slope = 0, Y-Intercept = 2 and X-Intercept = inf. Each value corresponds to the declared output fields.

Common Use Cases

  • Find y = mx + b equation from two points
  • Calculate slope and y-intercept
  • Convert standard form to slope-intercept form