Straight Lines
Q. What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
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A.
(1, 4)
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B.
(2, 7)
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C.
(3, 10)
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D.
(4, 13)
Solution
Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).
Correct Answer: A — (1, 4)
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Q. What is the slope of the line perpendicular to the line 3x + 4y = 12?
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A.
-3/4
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B.
4/3
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C.
3/4
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D.
-4/3
Solution
The slope of the line 3x + 4y = 12 is -3/4. The slope of the perpendicular line is the negative reciprocal, which is 4/3.
Correct Answer: B — 4/3
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Q. What is the slope of the line perpendicular to the line 4x + 3y = 12?
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A.
-3/4
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B.
4/3
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C.
3/4
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D.
-4/3
Solution
The slope of the line 4x + 3y = 12 is -4/3. The slope of the perpendicular line is the negative reciprocal, which is 3/4.
Correct Answer: D — -4/3
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Q. What is the slope of the line perpendicular to the line 5x + 2y = 10?
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A.
-2/5
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B.
5/2
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C.
2/5
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D.
-5/2
Solution
The slope of the line is -5/2. The slope of the perpendicular line is the negative reciprocal, which is 2/5.
Correct Answer: A — -2/5
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Q. What is the slope of the line perpendicular to the line 7x - 2y + 3 = 0?
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A.
1/2
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B.
-1/2
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C.
2
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D.
-2
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/2
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Q. What is the slope of the line perpendicular to the line 7x - 2y = 14?
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A.
1/7
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B.
-1/7
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C.
2/7
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D.
-2/7
Solution
The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.
Correct Answer: B — -1/7
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Q. What is the x-intercept of the line 5x - 2y + 10 = 0?
Solution
Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2.
Correct Answer: B — 2
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Q. What is the x-intercept of the line 6x - 2y = 12?
Solution
Setting y = 0 in the equation gives 6x = 12, thus x = 2. The x-intercept is 2.
Correct Answer: B — 3
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Q. What is the y-intercept of the line 4x + 5y - 20 = 0?
Solution
Setting x = 0 in the equation gives 5y = 20, thus y = 4. The y-intercept is 4.
Correct Answer: B — 5
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Q. Which of the following points lies on the line 4x - 5y + 20 = 0?
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A.
(5, 0)
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B.
(0, 4)
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C.
(4, 0)
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D.
(0, -4)
Solution
Substituting (0, -4) into the equation gives 4(0) - 5(-4) + 20 = 0, which is true.
Correct Answer: D — (0, -4)
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