Q. If the line 2x + 3y = 12 is transformed to slope-intercept form, what is the slope?
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A.
-2/3
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B.
2/3
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C.
3/2
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D.
-3/2
Solution
Convert to slope-intercept form (y = mx + b).\n1. 3y = -2x + 12\n2. y = -2/3x + 4.\nThe slope is -2/3.
Correct Answer:
A
— -2/3
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Q. What is the equation of the line perpendicular to y = 3x + 1 that passes through the point (2, 5)?
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A.
y = -1/3x + 7
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B.
y = 3x - 1
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C.
y = -3x + 11
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D.
y = 1/3x + 3
Solution
The slope of the given line is 3.\nThe slope of the perpendicular line is -1/3.\nUsing point-slope form: y - 5 = -1/3(x - 2) gives y = -1/3x + 7.
Correct Answer:
A
— y = -1/3x + 7
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Q. What is the equation of the line that passes through the points (1, 2) and (3, 6)?
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A.
y = 2x
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B.
y = 3x - 1
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C.
y = 4x - 2
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D.
y = x + 1
Solution
Calculate the slope: m = (y2 - y1)/(x2 - x1) = (6 - 2)/(3 - 1) = 2.\nUsing point-slope form: y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the slope of the line represented by the equation 2y - 4x = 8?
Solution
First, rewrite the equation in slope-intercept form (y = mx + b).\n1. 2y = 4x + 8\n2. y = 2x + 4.\nThe slope (m) is 2.
Correct Answer:
A
— 2
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Q. What is the solution set for the equation 2x + 3 = 7?
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A.
x = 2
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B.
x = 3
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C.
x = 4
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D.
x = 5
Solution
Subtract 3 from both sides: 2x = 4.\nThen divide by 2: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the x-intercept of the line given by the equation 4x - 2y = 8?
Solution
To find the x-intercept, set y = 0.\n1. 4x - 2(0) = 8\n2. 4x = 8\n3. x = 2.\nThe x-intercept is 2.
Correct Answer:
C
— 4
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Q. What is the y-intercept of the line given by the equation 3x + 2y = 6?
Solution
Convert to slope-intercept form (y = mx + b).\n1. 2y = -3x + 6\n2. y = -1.5x + 3.\nThe y-intercept is 3.
Correct Answer:
B
— 3
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Q. Which of the following is the correct factored form of the quadratic x^2 - 5x + 6?
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A.
(x - 2)(x - 3)
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B.
(x + 2)(x + 3)
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C.
(x - 1)(x - 6)
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D.
(x + 1)(x + 6)
Solution
To factor, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the factored form of the quadratic equation x^2 - 5x + 6?
-
A.
(x - 2)(x - 3)
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B.
(x + 2)(x + 3)
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C.
(x - 1)(x - 6)
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D.
(x + 1)(x + 6)
Solution
To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the factored form of x^2 - 5x + 6?
-
A.
(x - 2)(x - 3)
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B.
(x + 2)(x + 3)
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C.
(x - 1)(x - 6)
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D.
(x + 1)(x + 6)
Solution
To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Which of the following is the standard form of the equation of a line with slope 5 and y-intercept -3?
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A.
y = 5x - 3
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B.
5x + y = -3
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C.
y = -5x + 3
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D.
5x - y = 3
Solution
The slope-intercept form is y = mx + b.\n1. y = 5x - 3 can be rearranged to 5x - y = 3.\nThus, the standard form is 5x - y = 3.
Correct Answer:
B
— 5x + y = -3
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Q. Which of the following lines is parallel to the line y = -1/2x + 3?
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A.
y = 1/2x - 1
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B.
y = -1/2x + 1
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C.
y = 2x + 3
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D.
y = -2x + 3
Solution
Parallel lines have the same slope.\nThe slope of the given line is -1/2, so a parallel line must also have a slope of -1/2.
Correct Answer:
B
— y = -1/2x + 1
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Q. Which of the following represents the inequality x + 3 > 5?
-
A.
x > 2
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B.
x < 2
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C.
x > 8
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D.
x < 8
Solution
To solve x + 3 > 5, subtract 3 from both sides.\n1. x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following represents the inequality x + 3 > 7?
-
A.
x > 4
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B.
x < 4
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C.
x > 10
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D.
x < 10
Solution
Subtract 3 from both sides: x > 7 - 3.\nThus, x > 4.
Correct Answer:
A
— x > 4
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Q. Which of the following represents the line with a slope of -1 and a y-intercept of 4?
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A.
y = -x + 4
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B.
y = x + 4
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C.
y = -x - 4
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D.
y = x - 4
Solution
The slope-intercept form is y = mx + b.\nHere, m = -1 and b = 4, so the equation is y = -x + 4.
Correct Answer:
A
— y = -x + 4
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Q. Which of the following represents the standard form of a linear equation?
-
A.
y = mx + b
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B.
Ax + By = C
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C.
y = ax^2 + bx + c
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D.
x^2 + y^2 = r^2
Solution
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Correct Answer:
B
— Ax + By = C
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