If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? (There are several correct choices.)

Slope is a measure of the steepness or incline of a line, typically represented as a ratio of the vertical change (rise) to the horizontal change (run). In this case, the slope can be calculated by dividing the rise of 2.5 feet by the run of 10 feet, resulting in a slope of 0.25 or 25%.

Grade is often used interchangeably with slope, particularly in contexts like walkways or roads. It is expressed as a percentage, calculated by taking the slope (rise/run) and multiplying by 100. For the walkway in question, the grade would be 25%, indicating that for every 100 feet horizontally, the walkway rises 25 feet.

A ratio is a mathematical expression that compares two quantities, showing the relative size of one quantity to another. In the context of slope and grade, the ratio of rise to run (2.5 ft to 10 ft) is essential for determining the slope and can be simplified to express the relationship in various forms, such as a fraction or percentage.