Algebra 1
Chapter 5 Test Review
Name:_____________________
Assignment:________________
IMPORTANT INFORMATION THAT I PROMISE I WILL MEMORIZE FOR THE
TEST!!!!!
Slope is equal to ______________________ over ______________________
The Slope equation is m = ___________________________
Slope-Intercept form looks like:________________________________________
“m” stands for the _________________ and “b” stands for the ________________________
and the y-intercept is where my line crosses the _______________________
Point-Slope form looks like:________________________________________
Write the equations of the graphs sketched below.
1.
2.
3.
Graph the following equations.
4. x = 4
5.
6.
y=½
x = -2
Place two clear points on each graph, then fill in the missing information.
7.
8.
Slope of Line Shown:_________________
Slope of Line Shown:_______________
Slope of a Line Parallel to it:____________
Slope of a Line Parallel to it:_________
Slope of a Line Perpendicular to it:_________
Slope of a Line Perpendicular to it:____
9.
10.
Slope of Line Shown:_________________
Slope of Line Shown:_______________
Slope of a Line Parallel to it:____________
Slope of a Line Parallel to it:_________
Slope of a Line Perpendicular to it:_________
Slope of a Line Perpendicular to it:____
Use the line shown to write an equation of a line in SLOPE-INTERCEPT FORM. You DO NOT
need to make any calculations – just observe the graph for the missing information.
11.
12.
Slope:__________________
Slope:___________________
b:______________________
b:______________________
Equation:________________
Equation:________________
13.
14.
Slope:__________________
Slope:___________________
b:______________________
b:______________________
Equation:________________
Equation:________________
Use the following information to write an equation in SLOPE-INTERCEPT form.
5
15. m =
and b = 6
16. m = ½ and b = -12
3
Final Equation:_____________________________
Final Equation:_____________________________
Use the following information to write an equation. Begin by using point-slope form and be
sure your final answer is in slope-intercept form.
17. m = -2 and through (-3, 7)
18. m = 6 and through (0, -3)
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:___________________________
19. m = -1 and through (6, -2)
20. m = ½ and through (4, 8)
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
1
21. m =  and through (-2, -6)
3
22. m = 0 and through (-6, 7)
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
23. m = -5 and through (-4, -2)
24. m = 
2
and through (16, 4)
3
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
Writing the Equation of a Line Through TWO Points
1.
Use the slope formula ____________________________ to find m
2.
Use m, x1 and ______________ to write an equation in point-slope form
3.
Solve for y to put into slope-intercept form
Write an equation for the line that passes through the following points.
25. (2, 4) and (3, 6)
26. (-1, 5) and (2, 2)
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
27. (1, 2) and (0, -4)
28. (-3, -1) and (1, -9)
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
29. (2, 1) and (4, 2)
30. (-6, 7) and (-8, 8)
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
31. (5, 0) and (-10, -5)
32. (-6, -2) and (-10, -14)
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
Write an equation of the line shown in the graph. Your final answer should be in slopeintercept form.
33.
34.
Points
Points
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
35.
36.
Points
Points
Slope, m =
Slope, m =
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
Parallel and Perpendicular Lines
Parallel lines have the exact ______________________ slope
Perpendicular lines have opposite ____________________________ slopes
This means they have __________________ signs and the fraction is ________________
Determine if the following sets of lines are parallel, perpendicular, or neither.
Line 2: 2 y  4 x  6
Line 2: 2 y  4 x  1
2
x 1
3
Line 2: 3x  2 y  10
Slope 1:_____________
Slope 1:_____________
Slope 1:_____________
Slope 2:_____________
Slope 2:_____________
Slope 2:_____________
Relationship:_________
Relationship:_________
Relationship:_________
37. Line 1: y  2 x  4
38. Line 1: y  4 x  1
39. Line 1: y 
Determine if the following sets of lines are parallel, perpendicular, or neither.
1
4
40. Line 1: y  3x  6
41. Line 1: y   x  3
42. Line 1: y  x  9
2
5
Line 2:  2 y  6 x  4
Line 2: 2 y   x  4
Line 2: 5 x  4 y  8
Slope 1:_____________
Slope 1:_____________
Slope 1:_____________
Slope 2:_____________
Slope 2:_____________
Slope 2:_____________
Relationship:_________
Relationship:_________
Relationship:_________
Write an equation of the line with the following properties. Your final answer should be in
slope-intercept form.
1
43. Parallel to y  x  1 through (4, -1)
44. Parallel to y = 3x – 6 through (2, -3)
2
Slope Old Line:
Slope Old Line:
Slope New Line:
Slope New Line:
(x1, y1) New Line:
(x1, y1) New Line:
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
45. Parallel to 4 x  2 y  8 through (2, -5)
46. Parallel to y   x  2 through (8, -7)
Slope Old Line:
Slope Old Line:
Slope New Line:
Slope New Line:
(x1, y1) New Line:
(x1, y1) New Line:
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
47. Perpendicular to y  2 x  3 through (-4, 6)
48. Perpendicular to y   x  6 through (0, 11)
Slope Old Line:
Slope Old Line:
Slope New Line:
Slope New Line:
(x1, y1) New Line:
(x1, y1) New Line:
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
49. Perpendicular to y 
1
x  4 through (5, -6)
4
50. Perpendicular to y 
1
x  7 through (4, 1)
3
Slope Old Line:
Slope Old Line:
Slope New Line:
Slope New Line:
(x1, y1) New Line:
(x1, y1) New Line:
Point – Slope:_____________________________
Point – Slope:_____________________________
Final Equation:____________________________
Final Equation:____________________________
Standard Form
This means that the __________ and _____________ are on the left side of the equation
The first number cannot be a ________________________ or negative
Rewrite the following equations in standard form.
51. y  2 x  5
52. y  3x  7
Standard Form:__________________________
2
53. y   x  3
3
Standard Form:__________________________
54. y 
Standard Form:__________________________
55. y 
1
x2
4
Standard Form:__________________________
4
3
56. y   x 
5
5
Standard Form:__________________________
57. y 
1
x4
2
Standard Form:__________________________
5
x 1
7
Standard Form:__________________________
58.
1
x  2 y  3
4
Standard Form:__________________________
Decide whether each relation is a function. If, and only if, it is a function, give the domain and range.
Input Output
3
2
6
2
9
2
12
2
59. _____________
60. ____________
Input Output
3
1
6
5
3
2
12
8
61. _____________
62. _____________
_____________
_____________
_____________
_____________
_____________
_____________
_____________
_____________
Decide whether each graph shows a function. Respond with “Yes” or “No”
63. ___________
64. ___________
Evaluate the following functions as directed.
67. f(x) = 4 + 3x when x = 8
65. ___________
66. ___________
68. f(x) = ½x – 10 when x = 12
ANSWERS
1.
4.
y = -4
2.
5.
x = 2.5
3.
6.
x=0
7.
4
5
4
Parallel: 
5
Slope: 
Perpendicular:
5
4
8.
Slope:
1
2
Parallel:
9.
1
2
Slope:
1
4
Parallel:
Perpendicular: 
2
1
10. Slope: 
1
4
2
1
Parallel: 
Perpendicular: 
4
1
2
1
Perpendicular:
1
2
11. y   x  2
12. y 
1
x2
2
5
15. y   x  6
3
16. y 
1
x  12
2
17. y  2x  1
18. y  6 x  3
19. y   x  4
20. y 
1
x6
2
1
20
21. y   x 
3
3
22. y  7
23. y  5x  22
2
44
24. y   x 
3
3
25. m = 2; y  2x
26. m = -1; y  x  4
27. m = 6; y  6x  4
28. m = -2; y  2x  7
29. m = ½; y 
32. m = 3; y  3x  16
33. m = 1; y  x  3
31. m = ⅓; y 
1
5
x
3
3
2
13. y   x  1
3
35. m = -2; y  2x  1
36. m = 2; y  2 x  1
37. Slope 1: 2
38. Slope 1: 4
Slope 2: 2
Slope 2: 2
Parallel
Neither
40. Slope 1: 3
41. Slope 1: 
39. Slope 1:
1
30. m = -½; y   x  4
2
1
x
2
34. m = 1; y  x
2
3
3
2
Perpendicular
Slope 2: 
1
2
1
Slope 2: 
2
Parallel
Slope 2: -3
14. y  3x
42. Slope 1:
4
5
5
4
Perpendicular
Slope 2: 
Neither
1
43. y  x  3
2
44. y  3x  9
45. y  2x  1
46. y   x  1
1
47. y   x  4
2
48. y  x  11
49. y  4x  14
50. y  3x  13
51. 2x  y  5
52. 3x  y  7
53. 2 x  3 y  9
54. 5x  7 y  7
55. x  4 y  8
56. 4x  5 y  3
57. x  2 y  8
58. x  8 y  12
59. Yes! D:{-1, 0, 1}; R:{-7, -6, -5)
62. Yes! D:{-8, -4, 0}; R:{-2, -1, 0}
68. f(12) = -4
60. Yes! D:{3, 6, 9, 12}; R:{2}
63. Yes!
64. No
65. Yes!
61. No
66. No
67. f(8) = 28