Example 4.38 from Elementary Algebra, 4.4 Understand Slope of a Line

Understand Slope of a Line: example 4.38

The ‘pitch’ of a building’s roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is the slope of the roof shown?

This figure shows a house with a sloped roof. The roof on one half of the building is labeled "pitch of the roof". There is a line segment with arrows at each end measuring the vertical length of the roof and is labeled "rise equals 9 feet". There is a line segment with arrows at each end measuring the horizontal length of the root and is labeled "run equals 18 feet".

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Use the slope formula. $m = \frac{rise}{run}$

Substitute the values for rise and run. $m = \frac{9}{18}$

Simplify. $m = \frac{1}{2}$

The slope of the roof is $\frac{1}{2}$ .

The roof rises 1 foot for every 2 feet of horizontal run.

Table 4.40

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use Example 4.38, substituting the rise = 14 and run = 24.

How did it go?

Use the slope formula.	$m = \frac{rise}{run}$
Substitute the values for rise and run.	$m = \frac{9}{18}$
Simplify.	$m = \frac{1}{2}$
The slope of the roof is $\frac{1}{2}$ .
	The roof rises 1 foot for every 2 feet of horizontal run.

Solution

Your turn

Solution

Your turn