LineLab

Slope & Distance Calculator

Drop in two points — get slope, distance, midpoint, and the y = mx + b equation of the line through them.

x₁

y₁

x₂

y₂

Distance: 8.944
Slope (m): 2
Midpoint: (3, 6)
Equation: y = 2x + 0

slope = (y₂ − y₁) / (x₂ − x₁) = 2

Slope, distance and midpoint between two points

Slope is the rise over the run, distance comes from Pythagoras, and the line equation is y = mx + b.

Point 1	Point 2	Distance	Slope	Midpoint	Intercept b
(0, 0)	(3, 4)	5.0000	1.3333	(1.50, 2.00)	0.0000
(0, 0)	(6, 8)	10.0000	1.3333	(3.00, 4.00)	0.0000
(1, 2)	(5, 10)	8.9443	2.0000	(3.00, 6.00)	0.0000
(1, 1)	(4, 10)	9.4868	3.0000	(2.50, 5.50)	-2.0000
(2, 3)	(8, 3)	6.0000	0.0000	(5.00, 3.00)	3.0000
(-2, -3)	(4, 5)	10.0000	1.3333	(1.00, 1.00)	-0.3333

Rows one, two and six share a slope of 1.3333 while their distances range from 5 to 10 - slope describes direction only, so parallel lines of any length give the same value. Row five is horizontal, so the slope is zero and the intercept equals the shared y value. A vertical line would have an undefined slope, since the run is zero and the division is impossible. The 3-4-5 and 6-8-10 rows give whole-number distances because those are Pythagorean triples; most point pairs do not.

Quick formulas

Slope m = (y₂ − y₁) / (x₂ − x₁). Distance d = √((x₂ − x₁)² + (y₂ − y₁)²). Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

Frequently asked questions

How do I find the slope between two points?

Slope m = (y₂ − y₁) / (x₂ − x₁). For points (2, 3) and (6, 11): m = (11 − 3) / (6 − 2) = 8/4 = 2. A positive slope goes up-right, negative goes down-right, zero is horizontal, and undefined (division by zero) is vertical.

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

First find the slope: m = (y₂ − y₁) / (x₂ − x₁). Then use point-slope form: y − y₁ = m(x − x₁). Convert to slope-intercept: y = mx + b. For points (1, 2) and (3, 8): m = 3, so y − 2 = 3(x − 1) → y = 3x − 1.

What does a slope of 0 vs undefined mean?

Slope 0 = horizontal line (y doesn't change as x changes, like y = 5). Undefined slope = vertical line (x doesn't change, like x = 3). You can't write a vertical line in y = mx + b form because the slope would require division by zero.