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2.2 Answers 14. 563.00 euros 18. no 26. 1715 m in 5 sec. in air, so faster underwater 32. x – 2y = -3; A = 1, B = -2, C = -3 34. x – y = -6; A = 1, B = -1, C = -6 38. 5x – 4y = 2; A = 5, B = -4, C = 2 40. 6, -2 46. none, 4 48. 1, none 50. 6, -3 56. 1.75b + 1.5c = 525 58. yes, passes vert. line test

2.3 Notes Slope – rate of change 4 kinds of slopes: Δy y2 – y1 change in y Δx x2 – x1 change in x 4 kinds of slopes: positive negative zero undefined no slope

2.3 Note (con’t) What’s special about slopes of: Parallel lines? they are the same Perpendicular lines? they are opposites and reciprocals

Example 2 Use Slope to Graph a Line Example 3 Rate of Change Example 1 Find Slope Example 2 Use Slope to Graph a Line Example 3 Rate of Change Example 4 Parallel Lines Example 5 Perpendicular Line Lesson 3 Contents

Find the slope of the line that passes through (1, 3) and (–2, –3) Find the slope of the line that passes through (1, 3) and (–2, –3). Then graph the line. Slope formula and Simplify. Example 3-1a

Graph the two ordered pairs and draw the line. Use the slope to check your graph by selecting any point on the line. Then go up 2 units and right 1 unit or go down 2 units and left 1 unit. This point should also be on the line. (1, 3) Answer: The slope of the line is 2. (–2, –3) Example 3-1b

Answer: The slope of the line is Find the slope of the line that passes through (2, 3) and (–1, 5). Then graph the line. Answer: The slope of the line is Example 3-1c

Graph the line passing through (1, –3) with a slope of Graph the ordered pair (1, –3). Then, according to the slope, go down 3 units and right 4 units. Plot the new point at (5, –6). (1, –3) (5, –6) Draw the line containing the points. Example 3-2a

Graph the line passing through (2, 5) with a slope of –3. Answer: Example 3-2b

Communication Refer to the graph Communication Refer to the graph. Find the rate of change of the number of radio stations on the air in the United States from 1990 to 1998. Slope formula Substitute. Example 3-3a

Simplify. Answer: Between 1990 and 1998, the number of radio stations on the air in the United States increased at an average rate of 0.225(1000) or 225 stations per year. Example 3-3b

Answer: The rate of change is 2.9 million households per year. Computers Refer to the graph. Find the rate of change of the number of households with computers in the United States from 1984 to 1998. Answer: The rate of change is 2.9 million households per year. Example 3-3c

The x-intercept is –2 and the y-intercept is 2. Graph the line through (1, –2) that is parallel to the line with the equation The x-intercept is –2 and the y-intercept is 2. Use the intercepts to graph The line rises 1 unit for every 1 unit it moves to the right, so the slope is 1. (2, –1) (1, –2) Now, use the slope and the point at (1, –2) to graph the line parallel to Example 3-4a

Graph the line through (2, 3) that is parallel to the line with the equation Answer: Example 3-4b

The x-intercept is or 1.5 and the y-intercept is –1. Graph the line through (2, 1) that is perpendicular to the line with the equation The x-intercept is or 1.5 and the y-intercept is –1. Use the intercepts to graph 2x – 3y = 3 The line rises 1 unit for every 1.5 units it moves to the right, so the slope is or Example 3-5a

The slope of the line perpendicular is the opposite reciprocal of or Graph the line through (2, 1) that is perpendicular to the line with the equation 2x – 3y = 3 The slope of the line perpendicular is the opposite reciprocal of or (2, 1) Start at (2, 1) and go down 3 units and right 2 units. (4, –2) Use this point and (2, 1) to graph the line. Example 3-5b

Graph the line through (–3, 1) that is perpendicular to the line with the equation Answer: Example 3-5c

End of Lesson 3