Download CHAPTER 5 REVIEW QUESTIONS:

CHAPTER 5
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Name___________________________
rise y 2  y1
slope  m 

run x 2  x1
Slope Intercept Form: y = mx + b (b = y-intercept)
Point Slope Form: y  y1  mx  x1
Direct Variation: y = kx (line goes through the origin; k is a constant)
Standard Form: Ax + By = C
 have SAME slope
Parallel lines
Perpendicular lines have OPPOSITE RECIPROCAL slopes.
1. What is the slope of the line?
2. What is the general equation of any line
parallel to the y-axis?
A. y = k, where k is a constant
B. y = x
C. x = k, where k is a constant
D. y = 0
E. x = 0
(A)
1
3
(D) -1
(B) 1
(C) 
1
2
(E) -2
3. A line contains the points (-2, 4) and (2, -2). What is the slope of the line?
A. 
3
2
B. 
2
3
C.
2
3
D. 1
E.
1
2
3
2
4. What is the slope of the line perpendicular to the line y  x  6 ?
A. -2 B. 
1
2
C.
1
6
D.
1
2
E.
13
6
5. The slope of a line is 
A. y  
3
and the y-intercept is -3. What is the equation of the line?
4
3
x3
4
1
B. y   x  3
4
D. x  4 y  3
3
C. y   x  3
4
E. 4 x  3 y  3
6. What is the slope of a line parallel to 4x - 3y = 12?
A. -4
B. 
3
4
C.
1
4
D.
3
4
E.
4
3
7. What is the slope of a line perpendicular to 4x - 3y = 12?
A. 
3
4
B.
3
4
C.
1
4
D. -4 E.
4
3
8. What is the equation of a line that passes through (-6, 8) and is parallel to the x-axis?
A. x = -6
B. y = -6
C. x = 0
D. y = 8
E. x = 8
9. Which best describes the transformation from the graph of f (x ) = -x + 5 to the graph of f
(x ) = x + 6?
A. shifted 1 unit up and reflected over the x-axis
B. shifted 1 unit up and reflected over the y-axis
C. shifted 6 units up and reflected over the y-axis
D. shifted 6 units up and reflected over the x-axis
E. shifted 11 units up and reflected over the y-axis
10. What is the slope of line that would be perpendicular to line m ?
(A) 
3
2
(B) 
2
3
(C)
2
3
(D)
3
2
11. What is the equation of the line that is parallel to y = 4x + 1 and passes through the point
(-3, 4)?
A. y = 4x – 8
B. y = 4x – 7
C. y = 4x + 1
D. y = 4x + 16
E. y = 4x - 20
12. A line contains the point (8, -4) and has a slope of -2. What would be the equation of that
line in point-slope form?
A. y – 4 = -2(x + 8)
B. y = -2x + 12
C. 2x + y = 12
D. y + 4 = -2(x – 8)
E. y = -2x – 12
13. What is the slope of the line y = 2x + 3?
A.
1
2
B.
2
3
C. 1
14. What is the equation of this graph?
D. 2
A.
B.
C.
D.
y  2x
y  2 x
y  x  2
y  x2
1
2
15. Which line is perpendicular to y  x  5 ?
A. y  2 x
1
2
B. y   x  1
1
2
C. y  x  3
D. y  2 x  5
16. Identify the correct graphical representation of the equation of the line that passes
through (3, 4) whose slope is zero.
A.
B.
C.
D.
17. Determine the equation of a line passing through the point (1, –5) and perpendicular to
1
y   x 1.
2
A. y  2 x  3
B.
y  2x  7
C.
y  2 x  3
D.
y
1
x5
2
18. Determine the equation of a line passing through points (4, –3) and (–2, 6) in slopeintercept form.
3
2
A. y =  x  3
2
3
B. y =  x  6
3
2
C. y =  x  3
2
3
D. y =  x  3
19. Determine the equation of a line passing through point (–2, 4) and (2, 6) in point-slope
form.
1
(x – 2)
2
1
B. y + 6 = (x + 2)
2
A. y – 6 =
C. y – 6 = 2 (x – 2)
D. y + 6 = 2 (x + 2)
20. Determine the equations of a line passing through (2, 5) and parallel to the line y = 3x –3?
A. y = 3x + 1
B.
y = 3x – 1
C.
y = 3x + 5
D.
y = 3x + 2
21. A line has a slope of 
standard form?
A. x – 4y = 12
1
and a y-intercept of 3. What is the equation of the line in
4
B. x + 4y = -12
C. x + 4y = 12
D. x – 4y = -12
22. Determine the y-intercept of the line 4x + 5y = 8.
A. 2
B.
1
2
C.
5
8
D.
8
5
23. How do you know that this is not the graph for y =
1
x + 3?
3
A. The line is a graph of y = 3
B.
The line should go through (3, 0)
C.
The line should go through (0, –3)
D.
The line should rise from left to right since
there is a positive slope
24. What will happen to the graph of y = –3x + 5 if the –3 is changed to a –4?
A. The slope of the new graph will be steeper
B. The slope of the new graph will be less steep
C. The new graph will be shifted up on the y-axis
D. The new graph will be shifted down on the y-axis
25. What is direct variation? How do you identify from a graph and from an equation?
26. Determine the equation of a line passing through the point (3, 5) and parallel to the line
–2x + y = – 3.
1
2
A. y   x  6.5
B. y  2 x  1
C. y  2 x  6.5
1
2
D. y   x  3
27. Tell whether each graph represents a direct variation.
A.
x
y
1
B.
x
y
1
1
2
2
3
3
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C.
x
y
0
1
2
1
3
2
____________
D.
x
y
3
1
3
2
5
2
4
3
7
3
5
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28. Tell whether each graph represents a linear function.
A.
x
1
2
3
4
y
4
6
9
14
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B.
x
1
2
3
4
y
5
8
11
14
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C.
x
1
2
3
4
y
5
12
21
31
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D.
x
1
2
3
4
y
2
4
8
16
_____________
29. Find the slope of each line.
(a) 7x + y = 6
(b) x + 3y = 1
(c) 6x – 5y = -3
(d) x +
1
y
=
2
4
CHAPTER 6
1. Solve the following system of equations by graphing. Give the solution as an ordered pair.
2. Solve the system by substitution.
x  3y
a. 4 y  x  1

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2x  y  6
b. 
x  y  3
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3. Solve by elimination.
2x  3y  14
b. 
2x  y  10
x  3y  7
a. 
x  2y  8
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4. Solve by any method you would like but show all steps necessary.
x  y  0
a. 
3x  y  8
2 y  3x
b. 
 y  2 x  2
Graph and show the solutions of the given inequality.
1
3
5. y  x 1
6. 2x  3y  6
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Graph the solutions of the systems of inequalities. (Be sure to identify with shading)
y  2x 1
x  y  3
7. 
8. 
y  2x  4

x  2y  4
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Solve each system. Tell whether the system has no solution, infinitely many solutions, or
one solution. If the system has one solution, name the solution.
9.
y  x  3

x  y  4
y  3x  5
10. 
3x  y  5
 x  2 y  3 z  2

2 x  2 y  z  7
27. Solve
 x  y  2 z  4

A. (1, 1, -3)
C.
(1, 0, 1)
B. (1, -3, -1)
D.
(1, -2, 3)
28. The mass of 100 nails and 250 screws is 137.5 g. The mass of 250 nails and 100 screws is
149.5 g. What is the mass of a single nail and a single screw?