Questions tagged [slope]

For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.

In mathematics, the slope (or gradient) of a line is a number that describes both the direction and the steepness of the line. In the US and a few other countries the slop is denoted by the letter $m$ in the slope-intercept form of a line, $y=mx+b$.

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise". The line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan.

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Decrease at an Increasing rate

I need a formula that decreases at an increasing rate. I'm guessing that logarithm is involved in the answer. My criteria: A value of 20 must return a value of 20 (low bound) A value of 80 must return a value of 60 (high bound) The values are always…
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Is this line rising or declining?

Suppose, the white line in the picture (681x262 px) has the slope of 0.8107. And, suppose, (0,0) is at the upper left. Is it rising or declining? What factors determine this decision?
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