Parallel and Perpendicular Lines

Which of the following equations represents a perpendicular line to the equation y = -3x + 2?

• y = 3x + 2

• y = (1/3)x + b

• y = -3x - 2

• y = -3x + 1

Given the equation y = 4x - 1, which of the following equations represents a parallel line?

• y = 4x + 3

• y = -4x + 3

• y = 2x + 3

• y = -4x - 1

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

Given the equation y = -2x + 5, which of the following equations represents a perpendicular line?

• y = 2x + b

• y = -x + b

• y = -2x + b

• y = (1/2)x + b

Which of the following equations represents a parallel line to the equation y = -5x + 3?

• y = 5x + 7

• y = 5x - 3

• y = -5x + 7

• y = 5x + 3

Which of the following equations represents a perpendicular line to the equation y = 2x - 4?

• y = -2x - 4

• y = 2x + b

• y = -1/2x + b

• y = 2x + 4

Given the equation y = 3x + 2, which of the following equations represents a parallel line?

• y = 3x - 1

• y = -3x + 2

• y = 2x + 3

• y = 3x + 1

Which of the following equations represents a parallel line to the equation y = 2/3x - 1?

• y = 3/2x - 1

• y = 2/3x + 2

• y = 1/2x + 1

• y = -2/3x + 2

Which of the following equations represents a perpendicular line to the equation y = -1/2x + 3?

• y = 2x + b

• y = -1/2x + b

• y = 1/2x + b

• y = -2x + b

Answer explanation

The slope of the given line is 3. A parallel line has the same slope. Using the point (1, 4) in the equation y = 3x + b, we find b = 7. Thus, the equation is y = 3x + 7.

Answer explanation

The slope of the given line is -2. The slope of a line perpendicular to it is the negative reciprocal, which is \frac{1}{2}. Using point-slope form with point (3, -1), we find the equation is \(y = \frac{1}{2}x - \frac{7}{2}\).