Parallel & Perpendicular Lines

1.

Line A passes through points ( 0,9) and (6,5) Line B passes through points (-6,-3) and (0,-7) Are lines A and B parallel,perpendicular,or neither?
- A.
  
  Parallel
- B.
  
  Perpendicular
- C.
  
  Neither
Correct Answer
A. Parallel

Explanation
The two lines are parallel because their slopes are equal. The slope of line A can be calculated as (5-9)/(6-0) = -4/6 = -2/3. The slope of line B can be calculated as (-7-(-3))/(0-(-6)) = -4/6 = -2/3. Since both slopes are equal, the lines are parallel.

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2.

Line A passes through points ( 5,1) and (-2,6) Line B passes through points (-1,-1) and (5.5) Are lines A and B parallel,perpendicular,or neither?
- A.
  
  Parallel
- B.
  
  Perpendicular
- C.
  
  Neither
Correct Answer
C. Neither

Explanation
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. Line A has a slope of (6-1)/(-2-5) = -5/7. Line B has a slope of (-1-5.5)/(-1-5) = -6.5/-6 = 13/12. Since the slopes of the two lines are not equal, they are not parallel. Additionally, the product of their slopes (-5/7 * 13/12) is not equal to -1, so they are not perpendicular either. Therefore, the lines are neither parallel nor perpendicular.

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3.

Which equation is the equation of a line parallel to y = -3/5x + 6?
- A.
  
  Y = 5/3x + 3
- B.
  
  Y = -3/5x + 3
- C.
  
  Y = 5/3x + 6
- D.
  
  Y = 3/5x + 6
Correct Answer
B. Y = -3/5x + 3

Explanation
The equation y = -3/5x + 3 is the equation of a line parallel to y = -3/5x + 6 because it has the same slope (-3/5) as the given equation. The y-intercept (3) is different, but this does not affect the parallel nature of the lines.

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4.

Which equation is the equation of a line perpendicular to y = 4/5x + 6 ?
- A.
  
  Y = -5/4x - 17
- B.
  
  Y = 5/4x + 6
- C.
  
  Y = 4/5x + 1
- D.
  
  Y = -4/5x - 2
Correct Answer
A. Y = -5/4x - 17

Explanation
The equation of a line perpendicular to y = 4/5x + 6 would have a slope that is the negative reciprocal of 4/5. The negative reciprocal of 4/5 is -5/4. Therefore, the correct answer is y = -5/4x - 17.

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5.

Which equation is the equation of a line that is parallel to the x-axis and that passes through the point (-2, 5)?
- A.
  
  Y = 5x - 2
- B.
  
  Y = - 2
- C.
  
  Y = 5
- D.
  
  X = - 2
Correct Answer
C. Y = 5

Explanation
The equation y = 5 represents a line that is parallel to the x-axis because the y-coordinate remains constant at 5 regardless of the value of x. This line passes through the point (-2, 5) as the y-coordinate is indeed 5 when x = -2.

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6.

Which equation is the equation of a line that is parallel to the y-axis and that passes through the point (7, -3)?
- A.
  
  X = 7
- B.
  
  Y = - 3
- C.
  
  Y = 7x - 3
- D.
  
  X = - 3
Correct Answer
A. X = 7

Explanation
The equation x = 7 represents a vertical line that is parallel to the y-axis. This is because the value of x remains constant at 7, while the value of y can vary. Therefore, any point on this line will have an x-coordinate of 7. Since the equation passes through the point (7, -3), it satisfies the condition and is the correct answer.

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7.

Which equation is the equation of a line that is parallel to the line defined by y = -3x - 2 and that passes through the point (-2, -1)
- A.
  
  Y = -3x - 7
- B.
  
  Y = -3x + 5
- C.
  
  Y = 1/3x - 7
- D.
  
  Y = 1/3x + 5
Correct Answer
A. Y = -3x - 7

Explanation
The equation y = -3x - 7 is the equation of a line that is parallel to the line defined by y = -3x - 2 because it has the same slope (-3). Additionally, it passes through the point (-2, -1) which satisfies the equation.

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8.

Which equation is the equation of a line tghat is perpendicular to the line defined by 4x - 5y - 12 = 0 with a y-intercept = - 2
- A.
  
  Y = 4/5x - 2
- B.
  
  Y = -4/5x - 2
- C.
  
  Y = -5/4x - 2
- D.
  
  Y = 5/4x - 2
Correct Answer
C. Y = -5/4x - 2

Explanation
The equation of a line that is perpendicular to the line defined by 4x - 5y - 12 = 0 can be found by taking the negative reciprocal of the slope of the given line. The given line has a slope of 4/5, so the perpendicular line will have a slope of -5/4. The y-intercept remains the same, so the equation of the perpendicular line is y = -5/4x - 2.

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9.

Determine the equation of a line perpendicualr to -6x + 9y - 12 = 0 with the same y-intercept as the line defined by -8x + 2y - 6 = 0
- A.
  
  Y = 2/3x + 4/3
- B.
  
  Y = 2/3x + 3
- C.
  
  Y = -3/2x + 3
- D.
  
  Y = -3/2x + 4/3
Correct Answer
C. Y = -3/2x + 3

Explanation
The given question asks for the equation of a line that is perpendicular to -6x + 9y - 12 = 0. To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 6/9, which simplifies to 2/3. The negative reciprocal of 2/3 is -3/2.

The question also states that the line should have the same y-intercept as the line defined by -8x + 2y - 6 = 0. To find the y-intercept of this line, we set x = 0 and solve for y. By doing this, we find that the y-intercept is 3.

Therefore, the equation of the line perpendicular to -6x + 9y - 12 = 0 with the same y-intercept as -8x + 2y - 6 = 0 is y = -3/2x + 3.

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10.

Determine the value of k in the graph
- A.
  
  -1
- B.
  
  -2
- C.
  
  -3
- D.
  
  -4
Correct Answer
C. -3

Explanation
The value of k in the graph can be determined by looking at the position of the point on the y-axis. In this case, the point is located at -3 on the y-axis, so the value of k is -3.

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11.

Line A passes through points (-8,3) and (-6,7) Line B passes through points (-5,4) and (-3,3) Are lines A and B parallel, perpendicular, or neither?
- A.
  
  Parallel
- B.
  
  Perpendicular
- C.
  
  Neither
Correct Answer
C. Neither

Explanation
To determine whether lines A and B are parallel, perpendicular, or neither, we can examine the slopes of the lines.

For line A, the slope (m1) can be calculated as:

m1 = (y2 - y1) / (x2 - x1) = (7 - 3) / (-3 - (-8)) = 4 / 5

For line B, the slope (m2) can be calculated as:

m2 = (3 - 4) / (-3 - (-5)) = -1 / 2

Now, let's compare the slopes:

Lines A and B are neither parallel nor perpendicular because their slopes are not equal (not parallel) and the product of their slopes is not -1 (not perpendicular). They have different slopes, so they are neither parallel nor perpendicular to each other.

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Parallel & Perpendicular Lines

Line A passes through points ( 0,9) and (6,5) Line B passes through points (-6,-3) and (0,-7) Are lines A and B parallel,perpendicular,or neither?

Line A passes through points ( 5,1) and (-2,6) Line B passes through points (-1,-1) and (5.5) Are lines A and B parallel,perpendicular,or neither?

Which equation is the equation of a line parallel to y = -3/5x + 6?

Which equation is the equation of a line perpendicular to y = 4/5x + 6 ?

Which equation is the equation of a line that is parallel to the x-axis and that passes through the point (-2, 5)?

Which equation is the equation of a line that is parallel to the y-axis and that passes through the point (7, -3)?

Which equation is the equation of a line that is parallel to the line defined by y = -3x - 2 and that passes through the point (-2, -1)

Which equation is the equation of a line tghat is perpendicular to the line defined by 4x - 5y - 12 = 0 with a y-intercept = - 2

Determine the equation of a line perpendicualr to -6x + 9y - 12 = 0 with the same y-intercept as the line defined by -8x + 2y - 6 = 0

Determine the value of k in the graph

Line A passes through points (-8,3) and (-6,7) Line B passes through points (-5,4) and (-3,3) Are lines A and B parallel, perpendicular, or neither?