Selected Answers to Math 390 Review Exam 2
I. Simplify.
A. 8  3(12x  4)  2x = 8  36x + 12  2x = 20  38x
B. (25x + 9)  (55x + 23) = 25x + 9  55x  23 = 30x  14
II. Solve for x.
A. 5(3x  2) = 35
15x  10 = 35
15x  10 + 10 = 35 + 10
15x = 45
(15x)/15 = 45/15
x = 3
B. 16x  3(15x + 8)  6 = 3(5x  4)  4(8x  5)
16x  45x  24  6 = 15x  12  32x + 20
29x  30 = 17x + 8
29x  30 + 17x = 17x + 8 + 17x
12x  30 = 8
12x  30 + 30 = 8 + 30
12x = 38
(12x)/(12) = 38/(12)
x = 19/6
III. Write each of the following equations in explicit form
(i.e. solve for y) and find three solutions to the equation and then graph.
A. x + 2y = 1 x  y
x + 2y  x = 1  x 1  0
2y = 1  x 3  1
(2y)/2 = (1  x)/2 5  2
y = (1  x)/2
B. 2x  y = 4 x  y
2x  y  2x = 4  2x 2 8
y = 4  2x 0  4
y/(1) = (4  2x)/(1) 3  2
y = (4  2x)/(1)
C. y  3x = 0 x  y
y  3x + 3x = 0 + 3x 1  3
y = 3x 0  0
2  6
V. Complete the following statements.
A. To find the xintercept of a line set y = 0 and solve for x.
B. To find the yintercept of a line set x = 0 and solve for y.
C. Find the xintercept and the yintercept of each of the following
and then graph.
1. 4x + 3y = 12 4x  3y = 12
4x + 3(0) = 12 4(0)  3y = 12
4x + 0 = 12 0  3y = 12
4x = 12 3y = 12
x = 3 y = 4
Conclusion: The xintercept is 3 and the yintercept is 4.
2. 3x  15 = 15y 3x  15 = 15y
3x  15 = 15(0) 3(0)  15 = 15y
3x  15 = 0 0  15 = 15y
3x = 15 15 = 15y
x = 5 1 = y
Conclusion: The xintercept is 5 and the yintercept is 1.
VI. Write each of the following lines in slopeintercept form.
Determine the slope and yintercept of each of the following and then graph.
A. 2y + x = 6 B. 4y  12 = 0 C. 6x + 3y = 9
2y = x + 6 4y = 12 3y = 6x + 9
y = (x + 6)/2 y = 3 y = (6x + 9)/3
y = x/2 + 3 y = 0x + 3 y = 2x+ 3
m = 1/2 m = 0 m = 2
b = 3 b = 3 b = 3
VII. Given the following lines. Determine the slope of each line,
the slope of any line parallel to the given line, and the slope
of any line perpendicular to the line.
A. 3x  y = 1
y = 3x + 1
y = 3x  1
m = 3
Any line parallel to this line has slope 3.
Any line perpendicular to this line has slope 1/3.
B. 2y + 3x = 6
2y = 3x + 6
y = (3/2)x + 3
m = 3/2
Any line parallel to this line has slope 3/2.
Any line perpendicular to this line has slope 2/3.
VIII. Find the equation of each of the following lines. Express the equation of the form Ax + By + C = 0.
A. Using the point slope formula we obtain
y  3 = 5(x  (2))
y  3 = 5(x + 2)
y  3 = 5x + 10
0 = 5x  y + 13
B. Using the slope formula we obtain
m = (10  2)/(3  (1))
m = 8/4
m = 2
Using the point slope formula we obtain
y  2 = 2(x  (1))
y  2 = 2(x + 1)
y  2 = 2x + 2
0 = 2x  y + 4
C. Since parallel lines have the same slope we may use the point slope formula to obtain
y  (1) = 2(x  4)
y + 1 = 2x  8
0 = 2x  y  9
D. Since any line perpendicular to a line with slope 2 has slope 1/2 we may use the point
slope formula to obtain
y  (1) = 1/2(x  4)
y + 1 = 1/2x + 2
2y + 2 = x + 4
x + 2y  2 = 0
IX. See text for needed formulas.
X. A. Line one is parallel to line two if and only if m = n.
B. Line one is perpendicular to line two if and only if mn = 1.
XI. See answers in back of text book.
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