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# Graphs and equations

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For problems 1 - 7, simplify the following expressions.:

Problems 8 - 11: Solve each equation.

12. Solve the inequality and express the solution in interval notation.:
2(x - 4) < 3x + 8

Problems 13 - 18, Solve each system by the algebraic method of your choice (either substitution or addition/multiplication).

19. Find the a) slope and b) y-intercept of 3x - 4y = 12.

20. Find the a) slope and b) y- intercept of 4x - y = 12.

21. Suppose y varies directly as w. If y = 48 when w = 4, then what is y when w = 11?

22. If y varies inversely as v and y = 8 when v = 6, then what is y when
v = 24?

23. Find the a) x-intercept and b) y-intercept of 6x - 8y = 24.

24. Find the slope of the line which passes through the points (6,3) and (6,-4).

25. Find the slope of the line which passes through the points (-7,4) and (4, -2).

26. Write the equation in slope-intercept form of the line passing through (-1,-4) and (0,-6).

27. Write the equation in point-slope form of the line with the slope of 5 and passing through the point (4, -1).

Problems 28 - 35, solve the application:

28. Wendy has 52 coins consisting of nickels and pennies. The value of the coins is \$1.20. How many of each type does she have?
a) Give the system of equations for solving this situation.
b) Find the number of nickels and pennies.

30. A roll of plastic wrap which is 12" by 250 feet that sells for \$2.80 (including tax) or a restaurant-style roll of plastic wrap which is 18" by 1000 feet and sells for \$14.86.
a) Which roll is the better buy?
b) How much would you save?
(Support your answers with costs and square footage of the two rolls.)

31. Find the interest earned at the end of the first year by depositing \$4,750 in an account that pays 4.3% interest.

32. The outside dimensions of a picture frame are 39 inches by 29 inches. If its inside dimensions are 32 inches by 20 inches, find the area of the frame itself.

33. If you pay 32% of your income in taxes and your income after taxes is \$23,256, what is your gross (before taxes) income?

34. The Shelby County Emergency 911System usually receives about 100 calls each hour. On Monday, November 25, the system was down for 80 minutes. All incoming calls received a busy signal during that time.
a) Give the equation for solving this situation.
b) How many calls would you predict were not received by the Emergency 911 system while it was not operating? (This actually happened.)

35. Corporation Wally Mart allows each of its traveling employees an amount of money
per day for a hotel room and food expenses. One employee travels for 4 days and 4 nights and is allotted \$480 while another employee travels fro 3 days and 2 nights and is allotted \$270.
a) Give the system of equations for solving this situation.
b) Find the amount allowed for a hotel room and daily food expenses

For problems 36 - 40, solve the system by graphing. Choose the best graph and solution (a, b, c, or d). If your choice is incorrect, there is no partial credit for the problem unless you show your steps.

#### Solution Summary

This provides examples of simplifying expressions, solving equations and inequalities, and working with graphs.

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