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Name _______________________________ Date ____________________ Period _________ Review # 2: Lines and Systems Find the slope of the line that passes through each pair of points. 1. (-5, 1) and (4, -2) _____________________ 2. (5, 6) and (-7, 2) _____________________ 3. (-6, -1) and (-4, -7) _____________________ 4. (-2, 0) and (-8, 2) _____________________ 5. (-2, 2) and (-8, 2) _____________________ 6. List all pairs of parallel and perpendicular lines. Parallel _____________________ Perpendicular Graph each line. 7. Graph the line using the intercepts x - 3y = 9 x-int:___________ y-int:___________ _____________________ Review # 2 8. Graph the line using the intercepts 3x + 2y = 6 x-int:___________ y-int:___________ 9. Graph using the slope and y-intercept 3x - 2y = 8 slope-intercept form:__________ m = ______ b = _______ Write the equation of the line with the following conditions. 1 10. slope = , passes through (-1, 5) in standard form 3 _____________________ 11. parallel to 2x + y = 10, passes through (2, -2) in slope-intercept form _____________________ 12. perpendicular to 3x – 4y = 6, passes through (3, -2) in slope-intercept form _____________________ 13. passes through (2, -1) and (8, -5) in slope-intercept form _____________________ Review # 2 14. passes through (4, 2) and (4,-5) in standard form _____________________ 15. passes through (7, 5) and (-1, 5) in standard form _____________________ 16. in standard form 17. in slope-intercept form x 9 3 -6 -18 -27 y -3 -5 -8 -12 -15 x -8 -3 -1 2 5 y 19 9 5 -1 -7 _____________________ _____________________ 18. The graph of the function y = -2x – 5 is shown. If the graph is translated down 4 units, what is the equation of the new line? _____________________ EQUATIONS AND INEQUALITIES 19. 3x – 5 > 7 – 5x 20. 3(2x + 25) – 2(x – 1) = 78 21. –5 < -17 – 2x 5 22. 3x + 1 < 7 or 2x – 9 > 7 23. 5 2x 17 24. 7x 35 7 25. 4x 5 9 Solve each system by elimination. 19. 2x + 2y = 8 3x + 3y = 12 answer:_____________ Review # 2 20. 2x – 5y = 2 3x – 7y = 1 answer: ____________ Solve the following system by substitution. 21. 4x + y = -7 3x - y = 0 answer:_____________ 22. 2x + y = 6 3x + 4y = 4 answer:____________ Solve the following systems by graphing. 23. x – 4y = -12 2x + y = 2 answer:________ 24. -4x + 12y = -16 -3x + 9y = 3 answer: _______________ Review # 2 Solve each word problem using a system of equations. 25. Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 110 tickets were sold for a total of $615.00, how many tickets of each type were sold? Answer_________________________________________________________ 26. Your bank charges you a fixed monthly fee for banking there, and a charge for each check you write. One month you wrote 23 checks and were charged $16.70. The next month you wrote 18 checks and were charged $15.95. How much is your fixed monthly charge, and how much do they charge per check? Answer______________________________________________________________ 27. On the first night of a concert, Fish Ticket Outlet collected $67,200 on the sale of 1600 lawn seats and 2400 reserved seats. On the second night, the outlet collected $73,200 by selling 2000 lawn seats and 2400 reserved seats. Find the cost of each kind of seat. Answer__________________________________________________________________ Review # 2 Review. 28. Solve 9 – 4(2 – y) = 7y – (3 + y) _____________________ 29. Solve and graph 2x + 4 > -2 or -2x + 5 > 15 _____________________ 30. Solve and graph -11 < 3x – 2 < 16 _____________________ 31. Solve and graph x 4 9 _____________________ 32. Solve and graph 2x 6 8 _____________________ Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 1 3 1 3 -3 1 3 0 Parallel: 1 & 4 Perpendicular: 2 & 3 x-int: (9, 0) y-int: (0, -3) x-int: (2, 0) y-int: (0, 3) 3 y= x–4 2 10. x – 3y = -16 11. y = -2x + 2 4 12. y = x+2 3 2 1 13. y = x+ 3 3 14. x = 4 15. y = 5 16. x – 3y = 18 17. y = -2x + 3 18. y = -2x – 9 19. infinitely many 20. (-9, -4) 21. (-1, -3) 22. (4, -2) 23. (-.444, 2.889) 24. No solution 25. 80 adult, 30 student 26. $13.25 fixed charge, $0.15 charge per check 27. $15 lawn seats, $18 reserved seats 28. 2 29. x < -5 or x > -3 30. -3 < x < 6 31. x < -5 or x > 13 32. -7 < x < 1