1. Write the interval [0. 6) in set notation and graph it on the real line. 1. {x | 0 ≤ x < 6}
2. Given the equation y = 5x – 12, how will y change if x: a. Increases by 3 units? b. Decreases by 2 units? a. Since Δx = 3 and m = 5, then Δy, the change in y, is Δy = 3 • m = 3 • 5 = 15 b. Since Δx = –2 and m = 5, then Δy, the change in y, is Δy = –2 • m = –2 • 5 = –10
3. Find the slope of the line determined by the following pair of points: (2, 3) and (4, 1). For (2, 3) and (4, –1), the slope is
4. Find the slope of the line determined by the following pair of points: (0, -1) and (4, -1). For (0, - 1) and (4, –1), the slope is
5. Find the slope m and y-intercept (0,b) (when they exist) and draw the graph. y = 3x – 4
6. Find the slope m and y-intercept (0,b) (when they exist) and draw the graph
7. Find the slope m and y-intercept (0,b) (when they exist) and draw the graph. 2x – 3y = 12
8. Find the slope m and y-intercept (0,b) (when they exist) and draw the graph.
9. Find the slope m and y-intercept (0,b) (when they exist) and draw the graph.
10-14 Write an equation of the line satisfying the following conditions. If possible, write your answer in the form y = mx + b. Slope – 2.25 and y-intercept – 8.
11. Slope 5 and passing through the point ( -1,-2)
12. Horizontal and passing through the point (1.5, -4)
13. Vertical and passing through the point ( 1.5, - 4)
14. Passing through the points (1, -1) and (5, -1)
15.
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17. Show that y – y1 = m(x – x1) simplifies to y = mx + b if the point (x1,y1) is the y-intercept (0,b).
18. Business: Energy Usage A utility considers demand for electricity “low” if it is below 8 mkW (million kilowatts, “average” if it is at least 8 mkW but below 20 mkW, “high” if it is at least 20 mkW but below 40 mkW, and “critical” if it is 40 mkW or more. Express these demand leverls in interval notation. [Hint: the interval for “low” is [0,8).
19. Business: U.S. Computer Sales Recently, computer sales in the U.S. have been growing approcimately linearly. In 2001 sales were 55.2 million units, and in 2006 sales were 75.7 million units. a. Use the first and last (Year,Sales) data points (1,55.2) and (6,75.7) to find the linear relationship y = mx + b between x = Years Since 2000 and y = Sales (in millions). b. Interpret the slope of the line. c. Use the linear relationship to predict sales in the year 2015.