Section 3.4 More About Slope 241 Slope in Real-Life Settings Slope has many meaningful applications in real life. Slope is used to construct stairs, wheelchair ramps, highways, and roofs. It is also used to express the difficulty level of ski slopes. In these physical situations, the slope is often described in terms of rise and run. For other applications, slope is considered a rate. For instance, it can be used to represent the growth in population, a tax rate, and other rates of change. In these situations, we must state the slope as the change in the y-values over the change in the x-values. �� ������������������������ ������������������ Determine the slope described in each situation. 2a. The guidelines for constructing a wheelchair ramp state that the maximum slope should be 1 in. vertical distance for every 12 in. of horizontal distance. Express the maximum slope of a wheelchair ramp. 2b. The grade of a highway is the measure of the incline or steepness of the road. The grade is generally expressed as a percentage. The steepest road in the United States is Canton Avenue in Pennsylvania. The road rises 37 ft of vertical distance for each 100 ft of horizontal distance. What is the grade of the road? (Source: http://www.geographylists.com/list17y.html) 2c. The population of a town increases by 3000 people every year. Solutions 2a. The slope of the wheelchair ramp is m = vertical change horizontal change = rise run = 1 12 2b. The road rises 37 ft vertically for each 100 ft of horizontal change. So, the slope is m = vertical change horizontal change = rise run = 37 100 = 37% 2c. In real-life situations, time is generally used for the variable x. So, in this situation, population represents the variable y. Therefore, the slope is m = change in y change in x = 3000 1 = 3000 Student Check 2 Determine the slope described in each situation. a. The pitch of a roof is defined as the ratio of the vertical increase of the roof to its horizontal increase. If a roof rises 8 in. for each 12 in. it extends horizontally, what is the pitch? b. Ski Dubai is the first indoor ski resort in the Middle East. It has five ski runs with differing difficulty levels. The longest run is 400 m with a fall of approximately 60 m. What is the slope of this run? c. The value of a car decreases by $5000 each year. Parallel and Perpendicular Lines We will now turn our discussion to the comparison of two lines. Two lines are parallel if they never intersect. For lines to be parallel, they must have the same slope but different y-intercepts. Consider the graphs of the equations y = 3 4 x - 1 and y = 3 4 x + 3. These lines have the same slope, 3 4 . The lines have different y-intercepts, so the lines are parallel. Objective 2 ▶ Determine the slope in real-world applications. 2 2 4 4 –2 + = x y 3 34 –4 –2 –4 x y – 1 = x y 34 Objective 3 ▶ Determine if two lines are parallel or perpendicular. 12 in. 1 in.
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above