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Chapter 1

Chapter 1. Linear Functions. Section 1.1. Slopes and Equations of Lines. Figure 1. Figure 2. Figure 3. Your Turn 1. Find the slope of the line through (1,5) and (4,6). Figure 4. Your Turn 2. Find the equation of the line with x -intercept − 4 and y -intercept 6.

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Chapter 1

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  1. Chapter 1 Linear Functions

  2. Section 1.1 Slopes and Equations of Lines

  3. Figure 1

  4. Figure 2

  5. Figure 3

  6. Your Turn 1 Find the slope of the line through (1,5) and (4,6).

  7. Figure 4

  8. Your Turn 2 Find the equation of the line with x-intercept − 4 and y-intercept 6. Solution: Notice that b = 6. To find m, use the definition of the slope after writing the x-intercept as (− 4, 0) and y-intercept as (0,6). Substituting these values into y = mx + b, we have

  9. Your Turn 3

  10. Your Turn 4

  11. Figure 5

  12. Your Turn 5

  13. Your Turn 5 continued

  14. Your Turn 6

  15. Your Turn 6 continued

  16. Figure 6

  17. Figure 7

  18. Figure 8

  19. Figure 9

  20. Figure 10

  21. Section 1.2 Linear Functions and Applications

  22. Your Turn 1

  23. Your Turn 2(a) Suppose that Greg Tobin, manager of a giant supermarket chain, has studied the supply and demand for watermelons. He has noticed that the demand increases as the price decreases. He has determined that the quantity (in thousands) demanded weekly, q, and the price (in dollars) per watermelon, p, are related by the linear function (a) Find the quantity of watermelons demanded at a price of $3.30 per watermelon.

  24. Your Turn 2(b) Greg also noticed that the quantity of watermelons supplied decreased as the price decreased. Price p and supply q are related by the linear function (b) Find the quantity of watermelons supplied at a price of $3.30 per watermelon.

  25. Your Turn 3 Find the equilibrium quantity and price for the watermelons using the demand equation and the supply equation Solution: The equilibrium quantity is found when the prices from both supply and demand are equal. Set the two expressions for p equal to each other and solve. The equilibrium quantity is 8000 watermelons. The equilibrium price can be found by plugging the value of q = 8 into either the demand or the supply function. Continued

  26. Your Turn 3 continued The equilibrium price can be found by plugging the value of q = 8 into either the demand or the supply function. Using the demand function, The equilibrium price is $3.20.

  27. Figure 11

  28. Figure 12

  29. Your Turn 4 The marginal cost to make x batches of a prescription medication is $15 per batch, while the cost to produce 80 batches is $1930. Find the cost function C(x), given that it is linear. Solution: Since the cost function is linear, it can be expressed in the form C(x) = mx+b. The marginal cost is $15 per batch, which gives the value for m. Using x = 80 and C(x) = 1930 in the point-slope form of the line gives

  30. Your Turn 5 A firm producing poultry feed finds that the total cost C(x) in dollars of producing x units is given by Management plans to charge $58 per unit for the feed. How many units must be sold to produce a profit of $8030? Solution: Since R(x) = p x and p = 58, R(x) = 58x. Use the formula for profit P(x) = R(x) – C(x).

  31. Figure 13

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