Maths Coordinate geometry

Slope calculator

x₁

y₁

x₂

y₂

Slope 2

(8 − 2) ÷ (4 − 1) = 2

Line equation y = 2x + 0

Angle 63.435°

Grade 200%

Rise 6

Run 3

Distance between the points 6.7082

Midpoint (2.5, 5)

Live · rise over run, with the equation

Slope, angle and grade are three views of one thing

A slope of 2 means the line rises two units for every one across. That is 63.4° from horizontal and a grade of 200%. Road signs use grade, surveyors use degrees, and algebra homework wants the plain ratio.

Slope is rise over run: the change in y divided by the change in x. For the points (1, 2) and (4, 8) the rise is 6 and the run is 3, so the slope is 2 and the line is y = 2x. A vertical line has no slope at all, because its run is zero and division by zero is undefined.

How to use it

1 Enter the coordinates of the first point, then the second.

2 The slope appears at the top and the equation of the line just below it.

3 Angle, grade, distance and midpoint are all derived from the same two points.

The angle and the grade are easy to confuse. A 100% grade is a 45° slope, not a vertical wall — grade is the tangent of the angle expressed as a percentage. Roads are signed in grade, so a 10% hill climbs one metre for every ten travelled horizontally, an angle of 5.7°.

Questions

What if the two x values are the same? −

The line is vertical, the slope is undefined, and the equation is reported as x equals that value rather than as y = mx + b.

What does a negative slope mean? +

How is the distance worked out? +

Does the order of the points matter? +

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