How do you calculate the slope between two points?

Slope (m) = rise / run = (y₂ − y₁) / (x₂ − x₁). Subtract the y-coordinates to get the rise, subtract the x-coordinates to get the run, then divide. The order of subtraction must be consistent — if you start with point 2 for y, start with point 2 for x as well. For points (1, 2) and (4, 6): • Rise = y₂ − y₁ = 6 − 2 = 4 • Run = x₂ − x₁ = 4 − 1 = 3 • Slope m = 4/3 ≈ 1.3333 Interpreting the slope: • Positive slope: line rises from left to right (m > 0) • Negative slope: line falls from left to right (m < 0) • Zero slope: horizontal line (m = 0, y is constant) • Undefined slope: vertical line (x is constant, run = 0) • Steep lines have large |m|; gentle lines have small |m| • m = 1: line rises at exactly 45°

How do you find the equation of a line from two points?

First calculate the slope m = (y₂−y₁)/(x₂−x₁). Then find the y-intercept b by substituting one point into y = mx + b and solving for b: b = y₁ − m·x₁. The line equation is y = mx + b. For points (1, 2) and (4, 6): • m = (6−2)/(4−1) = 4/3 • b = 2 − (4/3)×1 = 2 − 4/3 = 6/3 − 4/3 = 2/3 • Line equation: y = (4/3)x + 2/3 Three equivalent forms of a line equation: • Slope-intercept form: y = mx + b (most common, shows slope and y-intercept) • Point-slope form: y − y₁ = m(x − x₁) (useful when you know slope and one point) • Standard form: ax + by = c (integers, no fractions — used in some textbooks) • All three forms describe the same line and can be converted between each other

What is the difference between parallel and perpendicular slopes?

Parallel lines have the same slope — they never intersect. Perpendicular lines meet at a right angle (90°) and their slopes multiply to −1 (they are negative reciprocals of each other). Parallel lines: • Same slope, different y-intercept: y=2x+3 and y=2x−1 are parallel • If m₁ = m₂, the lines are parallel • Parallel lines are always the same distance apart Perpendicular lines: • m₁ × m₂ = −1, so m₂ = −1/m₁ • If m₁ = 4/3, then m₂ = −3/4 • To find perpendicular slope: flip the fraction and change the sign • Special cases: a horizontal line (m=0) is perpendicular to a vertical line (undefined slope) • If m₁ = 2, perpendicular slope = −1/2 • If m₁ = −3, perpendicular slope = 1/3

How do you find the distance and midpoint between two points?

The distance formula uses the Pythagorean theorem: d = √((x₂−x₁)² + (y₂−y₁)²). The midpoint is the average of the x-coordinates and the average of the y-coordinates: M = ((x₁+x₂)/2, (y₁+y₂)/2). For points (1, 2) and (4, 6): • Distance = √((4−1)² + (6−2)²) = √(9+16) = √25 = 5 units • Midpoint = ((1+4)/2, (2+6)/2) = (2.5, 4) Why these formulas work: • Distance: the two points form the hypotenuse of a right triangle with legs Δx and Δy • Midpoint: averaging splits each coordinate exactly in half • The midpoint lies on the line segment and is equidistant from both endpoints • Distance is always positive; midpoint coordinates can be any real numbers

What does the angle of a slope mean?

The angle of inclination is the angle that the line makes with the positive x-axis, measured counterclockwise. It is calculated as θ = arctan(m), where m is the slope. The angle ranges from −90° (vertical, downward) to +90° (vertical, upward), with 0° being horizontal. Slope to angle conversions: • m = 0: θ = 0° (horizontal) • m = 1: θ = 45° (rises at 45°) • m = −1: θ = −45° (falls at 45°) • m = 4/3: θ = arctan(4/3) ≈ 53.13° • Undefined (vertical): θ = 90° Practical uses: • Road gradients: a 10% grade means m=0.1 → θ≈5.7° • Roof pitch: a 12/12 pitch means m=1 → θ=45° • Ramps: building codes often specify maximum angles (e.g. 4.76° for wheelchair ramps, m=1/12) • Sun angle: solar panels are angled at the local latitude for maximum efficiency

Slope Calculator — Line Equation, Angle, Distance & Midpoint

The Slope Calculator finds every property of a straight line from two points or from a point and slope. Two input modes: Two Points (enter (x₁,y₁) and (x₂,y₂)) or Point + Slope (enter one point and the slope m). Results include the slope as both a decimal and fraction, the line equation in slope-int...

SLOPE CALCULATOR

POINT 1 (x₁, y₁)

x₁

y₁

POINT 2 (x₂, y₂)

x₂

y₂

SLOPE (m)

4/3

LINE EQUATION

y = 4/3x + 0.6667

ANGLE

53.1301°

Y-INTERCEPT

0.666667

DISTANCE

MIDPOINT

(2.5, 4)

PARALLEL SLOPE

4/3

same slope

PERPENDICULAR SLOPE

-3/4

−1/m

↗ Positive slope — line rises left to right

STEP-BY-STEP

Points: (1, 2) and (4, 6)

Δy = 6 − 2 = 4

Δx = 4 − 1 = 3

Slope: m = Δy/Δx = 4/3 = 4/3

y-intercept: b = y₁ − m·x₁ = 2 − 4/3×1 = 0.666667

Line equation: y = 4/3x + 0.6667

Distance: √(Δx²+Δy²) = √(3²+4²) = √25 = 5

Midpoint: ((1+4)/2, (2+6)/2) = (2.5, 4)

QUICK EXAMPLES

COORDINATE PLANE

LINE PROPERTIES

Slope (rise/run)4/3 = 1.333333

Angle with x-axis53.1301°

y-intercept (0, b)(0, 0.666667)

x-intercept(-0.5, 0)

Point-slope formy − 2 = 4/3(x − 1)

Standard form4x − 3y = -2

Created with❤️byeaglecalculator.com

SLOPE FORMULAS

ALL SLOPE & LINE FORMULAS

NAME	FORMULA	DESCRIPTION
Slope formula	m = (y₂−y₁)/(x₂−x₁)	Rise over run between two points
Slope-intercept form	y = mx + b	m=slope, b=y-intercept
Point-slope form	y − y₁ = m(x − x₁)	Line through (x₁,y₁) with slope m
y-intercept	b = y₁ − m·x₁	Where the line crosses the y-axis
x-intercept	x = −b/m	Where the line crosses the x-axis
Distance	d = √((x₂−x₁)²+(y₂−y₁)²)	Pythagorean theorem on the two points
Midpoint	M = ((x₁+x₂)/2, (y₁+y₂)/2)	Centre point of the segment
Angle	θ = arctan(m)	Angle with positive x-axis in degrees
Perpendicular slope	m⊥ = −1/m	Negative reciprocal — product = −1
Standard form	ax + by = c	Integer coefficients, no fractions

HOW TO USE

1
Select your mode: Two Points if you know two coordinates, or Point + Slope if you know one point and the slope value.
2
Enter your values. For Two Points, enter (x₁, y₁) and (x₂, y₂). For Point + Slope, enter the point coordinates and the slope m.
3
The slope appears instantly as a fraction (where possible) and decimal. The line equation in y=mx+b form is shown alongside.
4
Check the coordinate plane — the line extends across the graph, both input points are marked with black dots, the midpoint in red, and the rise/run triangle is drawn with dashed lines.
5
The right panel shows all equivalent line forms: slope-intercept, point-slope, standard form, both intercepts, angle, and perpendicular/parallel slopes.

WORKED EXAMPLE

Example 1 (two points): (1,2) and (4,6). Rise=4, run=3, m=4/3≈1.3333. y-intercept: b=2−(4/3)(1)=2/3. Line: y=(4/3)x+2/3. Angle=53.13°. Distance=5. Midpoint=(2.5,4). Perpendicular slope=−3/4. Example 2 (point+slope): m=2, point (3,5). b=5−6=−1. Line: y=2x−1.

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

Rectangle Calculator

Calculate instantly →

Right Triangle Calculator

Calculate instantly →

Slope Between Two Points Calculator

Calculate instantly →

Cylinder Calculator

Calculate instantly →

MORE GEOMETRY CALCULATORS

Circle Calculator

Calculate instantly →

Triangle Calculator

Calculate instantly →

Right Triangle Calculator

Calculate instantly →

Rectangle Calculator

Calculate instantly →

Sphere Calculator

Calculate instantly →

Cylinder Calculator

Calculate instantly →

Slope Between Two Points Calculator

Calculate instantly →

Was this calculator helpful?

Last updated: April 29, 2026 · Formula verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.