y y Student Check 4 a. b. 4 2 3, 1 4 2, –1 –2 –4 –4 x x 5, 1 10, 0 4 4 8 8 12 16 –4 –8 SUMMARY OF KEY CONCEPTS 1. The slope and y-intercept have meaning when the linear equation represents a real-life situation. The y-intercept represents the initial value and the slope is a rate of change indicating how the y-values change as the x-values change. 2. Slope has many physical applications, such as the grade of a road, wheelchair ramps, and roofs. Slopes are also used to denote rates of change, such as a population rate. 3. Lines that have the same slope and different y-intercepts are parallel to one another. Lines that have slopes that are negative reciprocals are perpendicular to one another. GRAPHING CALCULATOR SKILLS The calculator can help us determine if lines are parallel or perpendicular. It is often helpful to graph the lines in the ZDecimal or ZSquare format so that the graphs are not distorted. Because of the possible distortion, it is best to compare the line’s slopes to determine how they relate to each other. Example: Are y = 2x - 3 and y = 1 2 x + 1 parallel, perpendicular, or neither? By graphing the lines on the calculator, we can verify that the lines are neither parallel nor perpendicular. Example: Are y = 2x - 3 and y=- 1 2 x + 1 parallel, perpendicular, or neither? The graphs show that the lines are perpendicular to one another. SECTION 3.4 EXERCISE SET Write About It! Interpret the meaning of the slope and y-intercept in the context of each situation. Use the slope and y-intercept to create a table of three ordered pairs that satisfy the given equation. (See Objective 1.) 1. The expenditure per student in fall enrollment for public elementary and secondary education in the United States can be approximated by the equation y = 374.15x + 7672.73, where x is the number of years after 2001. (Source: http://nces.ed.gov/programs/projections/ projections2018/tables/table_34.asp) 2. The total student enrollment (in thousands) in all degree-granting institutions (2-yr and 4-yr colleges and universities) can be approximated by the equation y = 351x + 16,121, where x is the number of years after 2001. (Source: http://nces.ed.gov/programs/projections/ projections2018/tables/table_10.asp) 3. The percentage of high school students who regularly smoke cigarettes is on the decline. The percentage of students who are smokers is given by the equation y = -2.5x + 38, where x is the number of years after 1997. (Source: National Cancer Institute) 4. The percent of U.S. adults aged 20 yr and over who were obese can be modeled by the linear equation y = 0.71x + 19.83, where x is the number of years after 1997. (Source: National Center for Health Statistics) 246 Chapter 3 Linear Equations in Two Variables
hendricks_beginning_intermediate_algebra_1e_ch1_3
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