If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its

step 1 On this problem, we want to identify which of the following expresses the slope of the given sit

If a walkway rises 2.5 ft for every 10 ft on the horizontal,...

If a walkway rises $2.5 \mathrm{ft}$ for every $10 \mathrm{ft}$ on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.) A. 25 B. 4 C. $\frac{2.5}{10}$ D. $25 \%$ E. $\frac{1}{4} \quad$ F. $\frac{10}{2.5}$ G. $400 \%$ H. $2.5 \%$ CAN'T COPY THE FIGURE

If a walkway rises $2.5 \mathrm{ft}$ for every $10 \mathrm{ft}$ on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.)
A. 25
B. 4
C. $\frac{2.5}{10}$
D. $25 \%$
E. $\frac{1}{4} \quad$
F. $\frac{10}{2.5}$
G. $400 \%$
H. $2.5 \%$
CAN'T COPY THE FIGURE

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Key Concepts

Slope

Slope is a measure of the steepness or incline of a line or surface, defined as the ratio of the vertical change (rise) to the horizontal change (run). This fundamental concept is used to quantify how quickly something is increasing or decreasing relative to its horizontal movement.

Grade

Grade refers to the steepness or incline, often expressed as a percentage. It represents how much the vertical height changes for every 100 units of horizontal distance, which directly connects to the concept of slope.

Ratio

Ratios are used to compare two quantities, such as the rise and run in slope problems. By expressing these quantities as a fraction, one can easily understand the relationship between the two, which is crucial when determining steepness.

Fraction to Percent Conversion

Converting a fraction to a percentage is a key concept, especially in expressing slopes as grades. Multiplying the fraction by 100 transforms the numerical value of the slope into a format that is more intuitive, such as a percentage, for interpreting steepness.

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