Student Tutorial: Slope Concepts: Definitions

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Study these terms and definitions related to the concept of slope.

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Slope. The ratio of the rise over the run, or the change in vertical distance over the change in horizontal distance.

Slope Formula. The equation used to find the slope m of a line, given two coordinates on the line.

Slope-Intercept Form. The equation of a linear function written in a form that easily identifies the slope (m) and y-intercept (b).

Positive Slope. A slope greater than zero. A line with a positive slope slants upward from left to right.

Negative Slope. A slope less than zero. A line with a negative slope slants downward from left to right.

Zero Slope. A line with a zero slope is horizontal. The change in the y-coordinates is zero.

Undefined Slope. A line with a undefined slope is vertical. The change in the x-coordinates is zero.

The Rise Over the Run. Another way of referring to slope: The ratio of the change in vertical distance over the change in horizontal distance.

Steepness. An informal way of referring to slope. Used to indicate the relative slope, rather than a specific value.

Pitch. The slope of a roof, usually expressed as a ratio with a denominator of 12.

Gradient. Another way of expressing slope. Often used to find the slope of a line tangent to a curve.

Grade. Slope expressed as a percent. Often used as a way to designate the steepness of a road.

“Delta x.” The change in x-coordinates found by subtracting the x-values of two coordinates. Often used with

“Delta y.” The change in y-coordinates found by subtracting the y-values of two coordinates. Often used

Slopes of Parallel Lines. Lines that are parallel have the same slope.

Slopes of Parallel Lines. Lines that are parallel have the same slope.