Algebra - Chapter 5 Review

Transcription

1 Name Hour Algebra - Chapter 5 Review 1. Write an equation in slope-intercept form of the graph. 10 y 10 x The cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What is the cost for 77 people? 3. Erik pays $225 in advance on his account at the athletic club. Each time he uses the club, $9 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 7 visits. 4. Write an equation of the line with slope and y-intercept Roman paid $150 to join a handball club. He pays an additional $15 every time he uses one of the club's handball courts. Write an equation that describes Roman's total cost for playing handball as a function of the number of times he plays. Let C = the total cost and n = the number of times he plays.

2 An amusement park charges $9.00 for admission and $4.00 per ride. Write an equation that gives the cost (in dollars) as a function of number of rides. 7. An airplane leaves its home airport and travels away at a constant speed. hours later it is 400 miles away. Write an equation giving its distance, D (in miles), at any time t (in hours). 8. Members of the soccer team are walking to raise money for a local shelter. 92 sponsors pledged a dollar per kilometer. Some sponsors gave additional donations that did not depend on the distance students walked. a. Write a verbal model that relates the total amount A of money raised by the soccer team to the number n of kilometers walked and the amount d given in additional donations. b. The team walked 8 kilometers and raised a total amount of $842. Is there enough information to find how much money came from additional donations that did not depend on walking distance? If so, find this amount. 9. Write an equation, in slope-intercept form, that passes through point with slope Write an equation of the line passing through the point with slope. 11. Write an equation of the line containing the points and.

3 12. Which is the equation for the linear function f in the form that has the given values?, 13. If a large factory sells its new gadgets for $5 each, it can sell 1050 per month, and if it sells the same gadgets for $9, it will sell 900 per month. Assuming the relationship between price and sales is linear, predict the monthly sales of gadgets to the nearest whole number if the price is $ Write an equation of a line: a. with slope 7 passing through the point. b. that passes through and has a slope of 5. c. containing and. 15. An editor gets a $2890 raise each year. In her third year, she is making $47,700 per year. Write an equation that gives her income as a function of how many years she has worked at the company.

4 16. The function represents the cost (in dollars) of ordering x t-shirts printed with a specialty logo. Which description best fits the function? a. The cost includes a $15 fee plus $10 for each t-shirt. b. The cost is $10 for each t-shirt. c. The cost is $15 for the first t-shirt and $10 for each additional t-shirt. d. The cost is $15 for each t-shirt. 17. Mary was told that a line goes through the points (1, 3) and (6, 2) and has a slope of 3. a. Explain why the information Mary was given cannot be correct. b. If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line. c. If the given points are correct for the line, what is the slope? Write an equation for the line. 18. A hospital's emergency electricity generator has a 200-gallon gas tank. The generator is controlled by a sensor that starts the generator as soon as a significant drop in electric voltage is detected. The graph below shows how many gallons of gasoline were in the tank when it was checked twice during a long power outage. Was the generator's tank full when the power outage occurred? Assume the generator uses gasoline at a steady rate.

5 19. Write the equation of the line passing through (2, 7), (2, 0), and (2, 5). 20. Write an equation of the line with undefined slope that passes through the point. 21. Write an equation, in point-slope form, a. of the line that passes through the point and has the slope 1 2. b. of the line that passes through the points and. 22. Write an equation in standard form for the line a. that passes through b. with 23. Write two equations in standard from that are equivalent to

6 24. Gregory ordered small trees to plant. The table below gives the cost of ordering different numbers of trees. In each case, the cost includes a shipping charge. Number of trees Total cost a. Explain why the situation can be modeled by a linear equation. b. Write an equation that gives the cost as a function of the number of trees shipped. What is the shipping charge? c. The company changes the shipping charge to $25. Write a new equation that gives the cost as a function of the number of trees shipped. 25. Graph the equation 26. The clearing house has resistors that sell for $3.50 each and circuit boards that sell for $2.25 each. Write an equation that represents how many of each type of electronic equipment can be bought with $7.

7 27. Write an equation of the line that passes through and is parallel to the line. 28. Write an equation of the line that goes through the point and is perpendicular to the line. 29. Make a scatter plot of the data in the table. Draw a line of fit. Write an equation of the line. x y Describe a scatter plot, and explain the difference between positive and negative correlation. 31. Use the graphing calculator to determine the equation of the best-fitting line and to approximate the value of y for x = 3. x y

8 32. The table below gives the number of hours a local baseball team spent on batting practice during each week and the number of hits they had in games that weekend. Number of hours Number of hits a) Use the graphing calculator to determine equation for the best- fitting line. b) Use your equation to predict the number of hits following a week when 20 h were spent on batting practice. c. How accurate is your prediction? Explain your reasoning. 33. The student council orders some T-shirts to sell at the school store. The number of school T-shirts available at the store can be modeled by the function, where x is the number of days the T-shirts have been on sale. a. Explain how to find the zero of the function. b. Explain what the zero means in this situation.