# Graphing, Trends and Forecasting

Please see the attached file for the complete questions.

Complete the ordered pairs so that each is a solution for the given equation.

24. (0, ), ( , ), ( ,0), ( , )

46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula . What is the Fahrenheit temperature that corresponds to each of the following Celsius temperatures: -10, 0, 15, 100?

48. Business and finance. When x number of units are sold, the price of each unit (in dollars) is given by . Find the unit price when the following quantities are sold: 2, 7, 9, 11.

Give the coordinates of the points graphed below.

2.

Give the coordinates of the points graphed below.

4.

23. Plot points with coordinates (2, 3), (3, 4), and (4, 5) on the given graph. What do you observe? Can you give the coordinates of another point with the same property?

Graph each of the following equations. (Please see the attached word document sheet it already has a template for a graph you can then copy and paste)

33 . 2x + 3y = 6

34. 2x - 3y = 12

50. Business and finance. The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item).

(a) If the fixed cost is $40 and the variable cost is $10, write the cost equation.

(b) Graph the cost equation.

(c) The revenue generated from the sale of x items is given by R = 50x. Graph the revenue equation on the same set of axes as the cost equation.

(d) How many items must be produced for the revenue to equal the cost (the break-even point)?

Find the slope of the line through the following pairs of points.

14. (-5, -3) and (-5, 2)

In Exercises 20 and 24, two points are shown. Find the slope of the line through the given points.

Find the slope of the lines graphed.

24.

25.

26.

In exercise 52, find the constant of variation k.

52. m varies directly with n; m = 144 when n =8.

64. Business and finance. The revenue for a sandwich shop is directly proportional to its advertising budget. When the owner spent $2000 a month on advertising, the revenue was $120,000. If the revenue is now $180,000, how much is the owner spending on advertising?

Use the following table for exercises 4 & 8.

World Motor Vehicle Production, 1950-1997

Production (in thousands)

Year United States Canada Europe Japan Other World Total

1997 12,119 2,571 17,773 10,975 10,024 53,463

1996 11,799 2,397 17,550 10,346 9,241 51,332

1995 11,985 2,408 17,045 10,196 8,349 49,983

1994 12,263 2,321 16,195 10,554 8,167 49,500

1993 10,898 2,246 15,208 11,228 7,205 46,785

1992 9,729 1,961 17,628 12,499 6,269 48,088

1991 8,811 1,888 17,804 13,245 5,180 46,928

1990 9,783 1,928 18,866 13,487 4,496 48,554

1985 11,653 1,933 16,113 12,271 2,939 44,909

1980 8,010 1,324 15,496 11,043 2,692 38,565

1970 8,284 1,160 13,049 5,289 1,637 29,419

1960 7,905 398 6,837 482 866 16,488

1950 8,006 388 1,991 32 160 10,577

Note: As far as can be determined, production refers to vehicles locally manufactured.

Source: American Automobile Manufacturers Assn.

4. What was the percentage increase in motor vehicle production in countries outside the United States from 1950 to 1997?

8. Between 1950 and 1997, did the production of motor vehicles increase by a greater percentage in Canada or Europe?

The following pie chart represents the way a new company ships its goods. Use the information presented to complete exercise 12.

Second day air freight 40%

Next day air freight 15%

Truck 45%

12. If the company shipped a total of 550 items last month, how many were shipped using second-day air freight?

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#### Solution Summary

The solution details the graphing of straight line equations, as well as calculations to obtain slope. Some percentage and business math problems are also solved.

Graphing, Trends and Forecasting

5.

(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992-2003 only. Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your choice to the 1992-2003 data. (f) Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set? Airplanes

Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set? Airplanes

U.S. Manufactured General Aviation Shipments, 1966-2003

Year Planes

1966 15,587

1967 13,484

1968 13,556

1969 12,407

1970 7,277

1971 7,346

1972 9,774

1973 13,646

1974 14,166

1975 14,056

1976 15,451

1977 16,904

1978 17,811

1979 17,048

1980 11,877

1981 9,457

1982 4,266

1983 2,691

1984 2,431

1985 2,029

1986 1,495

1987 1,085

1988 1,143

1989 1,535

1990 1,134

1991 1,021

1992 856

1993 870

1994 881

1995 1,028

1996 1,053

1997 1,482

1998 2,115

1999 2,421

2000 2,714

2001 2,538

2002 2,169

2003 2,090