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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 39
Chapter 3, Problem 39

If a walkway rises 2.5 ft for every 10 ft on the horizontal, which of the following express its slope (or grade)? <Image>
A. 0.25, B. 4, C. 2.5/10, D. 25%, E. 1/4, F. 10/2.5, G. 400%, H. 2.5% 

Verified step by step guidance
1
Understand that the slope (or grade) of a walkway is the ratio of the vertical rise to the horizontal run. In this problem, the walkway rises 2.5 ft vertically for every 10 ft horizontally.
Write the slope as a fraction: \(\frac{\text{rise}}{\text{run}} = \frac{2.5}{10}\).
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. Here, divide both 2.5 and 10 by 2.5 to get \(\frac{1}{4}\).
Express the slope as a decimal by performing the division \(\frac{2.5}{10} = 0.25\).
Optionally, express the slope as a percentage by multiplying the decimal by 100, so \(0.25 \times 100 = 25\%\) grade.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope as a Ratio

Slope represents the steepness of a line and is calculated as the ratio of vertical change (rise) to horizontal change (run). In this problem, the slope is the rise of 2.5 ft divided by the run of 10 ft, giving a numerical value that describes the incline.
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Slope as a Percentage Grade

The slope or grade can also be expressed as a percentage by multiplying the slope ratio by 100. This converts the ratio into a percent, which is commonly used to describe inclines in real-world contexts like walkways or roads.
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Unit Consistency and Interpretation

Ensuring that the units for rise and run are consistent is essential for correctly calculating slope. Here, both are in feet, so the ratio is dimensionless. Understanding how to interpret this ratio in different forms (fraction, decimal, percentage) helps in selecting correct expressions of slope.
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