Slope From Two Points: Rise Over Run, With Units

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Opens on Chapter 12’s example: Otto’s delivery log: 70 miles after 2 hours, 175 miles after 5 hours.

First point: x

Second point: x

Units of x

Units of y

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Enter your numbers, then press Work it out.

How it works

Rise is the change in y (second minus first), run is the change in x (in the same order), and slope is rise ÷ run. With units it reads as a rate: miles per hour, dollars per sheet. A negative slope falls from left to right; a run of zero is a vertical line, whose slope is undefined. Following the line back to x = 0 gives its starting value, y₁ − slope × x₁; where it reaches y = 0 is starting value ÷ (−slope).

From the book, Chapter 12. Otto rises 105 miles over 3 hours: 35 mph. The ramp’s slope is 1/12, about 8.3%. Sanjay’s prices rise $0.40 a sheet over a $12 setup. The tank falls −40 gallons an hour and is empty after 10 hours. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.