Find the slope, distance between two points, midpoint, and line equation — with every step of the math shown. Works as a standalone distance calculator too.
Slope is the change in y divided by the change in x between two points. This calculator also derives the distance between the points, their midpoint, and the full line equation.
Slope measures how steep a line is and in which direction it moves. A positive slope rises left to right, a negative slope falls, a zero slope is flat, and an undefined slope is vertical.
Example: for points (1,2) and (4,11), slope = (11-2)/(4-1) = 3, distance ≈ 9.49, midpoint = (2.5, 6.5).
| Point 1 | Point 2 | Slope |
|---|---|---|
| (0,0) | (2,4) | 2 |
| (1,2) | (4,11) | 3 |
| (3,5) | (3,9) | Undefined |
What is the slope formula? Slope = (y₂ - y₁) ÷ (x₂ - x₁), the change in y divided by the change in x between two points.
How do you find the slope between two points? Subtract the y-coordinates and the x-coordinates separately, then divide the difference in y by the difference in x. For (1,2) and (4,11), slope = (11-2)/(4-1) = 3.
What does a slope of zero mean? A slope of zero means the line is perfectly horizontal — the y-value doesn't change as x changes.
What does an undefined slope mean? The slope is undefined when the line is perfectly vertical, since the change in x is zero and division by zero is undefined.
How do you find the midpoint between two points? Average the x-coordinates and average the y-coordinates separately: midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
How do you write the equation of a line from two points? Find the slope first, then substitute one point into y = mx + b and solve for b (the y-intercept).
Example 1 — Positive slope: (1,2) to (4,11) → slope = 3, distance ≈ 9.49, midpoint = (2.5, 6.5).
Example 2 — Negative slope: (0,10) to (5,0) → slope = -2, line equation y = -2x + 10.
Example 3 — Vertical line: (3,5) to (3,9) → slope is undefined since x doesn't change.