📈 Geometry Tool

Slope Calculator

Find slope, y-intercept, angle, distance and line equation from two points — slope-intercept form, point-slope form and standard form, with a plotted graph.

Point 1 (x₁, y₁)

x₁

y₁

Point 2 (x₂, y₂)

x₂

y₂

Examples:

📈 Slope (m)

— —

Slope-intercept form 📋 —

Point-slope form 📋 —

Standard form (Ax + By = C) 📋 —

Perpendicular line slope 📋 —

—Slope m

—Y-intercept b

—Angle (°)

—Distance

↗️Positivem > 0

↘️Negativem < 0

➡️Zerom = 0

⬆️Undefinedvertical

📝 Step-by-step solution

Line graph

💡

Key insight

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Slope formulas

The slope of a line through two points (x₁,y₁) and (x₂,y₂) is the ratio of the vertical change (rise) to the horizontal change (run):

Slope: m = (y₂ − y₁) / (x₂ − x₁) = rise / run
Y-intercept: b = y₁ − m × x₁
Slope-intercept: y = mx + b
Point-slope: y − y₁ = m(x − x₁)
Distance: d = √((x₂−x₁)² + (y₂−y₁)²)
Angle: θ = arctan(m) in degrees
Perpendicular: m_perp = −1/m

Frequently asked questions

What does slope mean?

Slope (m) measures how steep a line is — specifically how much y changes for every 1 unit increase in x. A slope of 2 means y increases by 2 for every 1 step right. Slope = rise ÷ run.

What is a negative slope?

A negative slope means the line goes downward from left to right. As x increases, y decreases. For example, a slope of −3 means y decreases by 3 for every 1 unit increase in x.

What is an undefined slope?

A vertical line has undefined slope because both points have the same x-coordinate, making the denominator (x₂−x₁) equal to zero, which is division by zero. Vertical lines cannot be expressed in y = mx + b form.

How are perpendicular slopes related?

Two perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope m, the perpendicular line has slope −1/m. Their product is always −1. Horizontal (m=0) and vertical (undefined) lines are perpendicular to each other.