Slope Calculator: Rise Over Run & y=mx+b

Slope Calculator: Find Slope, Distance, Angle & Line Equation

How to find slope from two points. Free slope calculator with rise over run formula, distance between two points, angle in degrees and radians, and line equation y = mx + b. Solve for missing point from slope + distance.

What This Slope Calculator Does & Who It's For

Calculator Purpose & Ideal Users

This slope calculator finds slope, distance, angle, and the line equation from two points (x₁,y₁) and (x₂,y₂). Enter both points for direct computation, or Point 1 plus slope and distance to solve for Point 2. Used in algebra, geometry, pre-calculus, and graphing.

What You'll Get:

Slope as decimal and simplified fraction (rise over run), distance via √[(x₂−x₁)²+(y₂−y₁)²], angle θ in degrees and radians, line equation in slope-intercept form (y = mx + b). Logic Trace shows formula substitution step-by-step; a coordinate plot highlights Run (Δx) and Rise (Δy).
Ideal Users:

Students & algebra/geometry: How to find slope between two points, verify homework, see rise over run. Teachers: Demonstrate the slope formula with a visual plot. Pre-calculus & graphing: Get y = mx + b from two points. Anyone: Quick slope from two points calculator with distance and angle.
Scope & Limits:

2D Cartesian coordinates. Vertical lines (undefined slope) show x = k. Same point returns no result. All calculations run locally, no data stored.

Slope Formula: Rise Over Run & How to Find Slope

The slope of a line is rise over run: vertical change divided by horizontal change. The formula is:

m = \frac{y_2 - y_1}{x_2 - x_1}

where (x₁,y₁) and (x₂,y₂) are two points on the line. How to find slope: subtract the y-coordinates (rise), subtract the x-coordinates (run), then divide. Example: (1,3) and (4,9) → m = (9−3)/(4−1) = 6/3 = 2. Positive slope rises left-to-right; negative slope falls. A horizontal line has slope 0; a vertical line has undefined slope (run = 0).

How to Use This Calculator

Enter two points or one point plus slope and distance to find slope, distance, angle, and the line equation.

Point 1 (x₁, y₁) & Point 2 (x₂, y₂):

Type coordinates for both points. The dashboard returns slope (decimal and fraction), distance, angle θ, and the line equation in y = mx + b form.
Solve for Point 2:

Alternatively, enter Point 1, a slope (m), and a distance (d). The calculator finds the second point at that distance along the line.
Slope Output:

Displayed as a decimal and a simplified fraction (rise/run). Vertical lines show "Undefined" since run equals zero.
Line Equation:

Slope-intercept form y = mx + b for non-vertical lines. Vertical lines display x = k instead.
Logic Trace & Plot:

The Logic Trace shows each formula substitution step by step. The coordinate plot highlights Run (Δx) and Rise (Δy) visually.

Distance Between Two Points & Angle θ

The distance between two points uses the Pythagorean theorem:

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

The angle θ from the positive x-axis is θ = atan2(Δy, Δx) in radians; multiply by 180/π for degrees. This calculator returns both when you enter two points.

Slope-Intercept Form: y = mx + b

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Given two points: (1) find m = (y₂−y₁)/(x₂−x₁), (2) then b = y₁ − m·x₁. For vertical lines (undefined slope), the equation is x = k. This tool shows the line equation automatically.

Solving for a Missing Point from Slope and Distance

Given Point 1 (x₁,y₁), slope m, and distance d, Point 2 lies at distance d along the line. The unit direction vector is (1/√(1+m²), m/√(1+m²)), so x₂ = x₁ + d/√(1+m²) and y₂ = y₁ + m·d/√(1+m²). Enter Point 1, slope, and distance in the calculator to get Point 2; the Logic Trace shows the derivation.

Real-World Use: Graphing, Construction & Surveying

Slope appears in graphing linear equations, roof pitch and ramp grade (rise over run as percentage), and surveying (elevation change over horizontal distance). Carpenters use slope for roof design; engineers for road grades. This slope from two points calculator helps students check work and professionals verify coordinates quickly.

Slope Calculator FAQ

What is the slope of a line?

The slope (m) equals rise over run: m = (y₂ − y₁)/(x₂ − x₁). Positive slope rises left-to-right; negative slope falls. Vertical lines have undefined slope.

How do you find the slope between two points?

Use m = (y₂ − y₁)/(x₂ − x₁). Subtract the y-coordinates (rise), subtract the x-coordinates (run), then divide. Example: (2,5) and (4,9) → m = (9−5)/(4−2) = 2.

What is slope-intercept form?

y = mx + b, where m is the slope and b is the y-intercept. Given two points, compute m first, then b = y₁ − m·x₁. Vertical lines use x = k instead.

How do you find the distance between two points?

d = √[(x₂−x₁)² + (y₂−y₁)²] (Pythagorean theorem). This calculator also finds distance and the line equation. Enter both points or Point 1 + slope + distance to solve for the second point.

Slope Calculator