Slope Calculator
Give two points and the calculator works out the slope as rise over run, then hands you the rest of what those two points determine: the line itself, the angle it makes, the distance between them and the midpoint.
How it works
How the Slope Calculator works
the part a result on its own leaves out
What the slope tells you
Slope is the vertical change divided by the horizontal change — rise over run. One number carrying two facts: the sign says which way the line leans, and the size says how steeply. Any two points on the same line give the same value, because it is a ratio.
Why the vertical case is different
When both points share an x value the run is zero, and nothing can be divided by zero. The slope is undefined, not infinite and not zero, and the calculator says so rather than returning a number that would be wrong.
Common mistakes
Common mistakes with slope
the errors that actually show up, not every possible slip
Putting run over rise
Slope is the y difference on top. Inverting it gives the reciprocal, which is a much shallower or steeper line that still looks like a plausible answer.
Reversing the subtraction on one side only
(y₂ − y₁) over (x₁ − x₂) flips the sign. Both differences must be taken in the same order.
Confusing zero slope with undefined slope
A horizontal line has slope zero. A vertical line has undefined slope. Swapping them is the most common error in this topic.
Questions
Asked often enough to answer here
answers that change how you work
What is the formula for slope?
m = (y₂ − y₁) / (x₂ − x₁) — the difference in the y values divided by the difference in the x values, taken in the same order.
Does it matter which point I enter first?
No. Swapping the two points reverses both the top and the bottom of the fraction, so the slope comes out the same.
What does the angle of inclination mean?
The angle the line makes with the horizontal, found as arctan of the slope. A slope of 1 is 45°; a steeper line gives a larger angle.
What is the perpendicular slope?
The negative reciprocal. Flip the fraction and change the sign, so the two slopes multiply to −1.
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