The U.S. Department of Transportation requires surveyors to...

The U.S. Department of Transportation requires surveyors to place signs on steep sections of roads. The grade of a road is measured as a percent. For instance, the grade of the road shown below is $6 \% .$ What is the slope of the road? Explain the relationship between road grade and slope.

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Key Concepts

Slope

Slope is a measurement of how steep a line or surface is, defined as the ratio of the vertical change (rise) to the horizontal change (run). This concept applies broadly across mathematics and real-world scenarios, including engineering and physical geography, where it helps quantify inclines or declines.

Percent Grade

Percent grade is a way to express the steepness of a road or surface as a percentage, calculating the ratio of the rise to the run multiplied by 100. It is a practical, intuitive measure often used in transportation and civil engineering to indicate how steep a road is.

Relationship Between Road Grade and Slope

The relationship between road grade and slope is that the numerical value of the slope is the percent grade divided by 100. For example, a road with a 6% grade has a slope of 0.06, meaning that for every unit of horizontal distance, the vertical elevation changes by 0.06 units. This conversion allows one to readily move between the two representations depending on context.

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