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