Question

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part one: multiple choice - choose the best response and put the answer in the space provided on your answer sheet. (1 mark each)

1. a wheelchair ramp rises 7 feet over a distance of 28 feet. what is the slope of this ramp?

1. a staircase has a rise of 2.86 m over a run of 1.42 m. what is the slope of this staircase?

1. a skateboard rail rises 7 feet over a run of 12 feet. what is the length of the rail?

1. what is the slope of a line that includes (7, 12) and (21, 48) as coordinates?

1. how can you tell if a graph has a large slope?

Explanation:

Calculate the slope of the wheelchair ramp

The slope is defined as the ratio of rise to run.
Using the Right Triangle Trigonometry concept:

$$ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{7\text{ ft}}{28\text{ ft}} = 0.25 $$

Calculate the slope of the staircase

The slope is the ratio of rise to run.

$$ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{2.86\text{ m}}{1.42\text{ m}} \approx 2.01 $$

Calculate the length of the skateboard rail

The rail forms the hypotenuse of a right triangle with a rise of \(7\text{ ft}\) and a run of \(12\text{ ft}\).
Using the Pythagorean theorem:

$$ c = \sqrt{a^2 + b^2} = \sqrt{7^2 + 12^2} = \sqrt{49 + 144} = \sqrt{193} \approx 13.89\text{ ft} $$

Calculate the slope of the line through the given coordinates

The slope \(m\) between points \((x_1, y_1) = (7, 12)\) and \((x_2, y_2) = (21, 48)\) is:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{48 - 12}{21 - 7} = \frac{36}{14} = \frac{18}{7} \approx 2.57 $$

Determine how to identify a large slope on a graph

A graph has a large slope if the line is very steep.

Answer:

No.	Answer
2	\(\approx 2.01\)
3	\(\approx 13.89\text{ ft}\)
4	\(\frac{18}{7}\) (or \(\approx 2.57\))
5	The line on the graph is very steep.