Answered

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Determine whether each pair of lines is perpendicular, parallel, or neither.
2y = 4x + 4
y=-2x-2
4y= 2x - 4
y=-2x+9
Perpendicular
Parallel
y = 2x+4
2y = 4x - 7
Neither

Sagot :

sqdancefan

Answer:

  • neither
  • perpendicular
  • parallel

Step-by-step explanation:

You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.

Parallel

Parallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.

Perpendicular

Perpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.

Application

1. 2y = 4x +4; y = -2x -2

Solving the first equation for y gives ...

  y = 2x +2

The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.

2. 4y = 2x -4; y = -2x +9

Solving the first equation for y gives ...

  y = 2/4x -1 = 1/2x -1

The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.

3. y = 2x +4; 2y = 4x -7

Solving the second equation for y gives ...

  y = 2x -7/2

The x-coefficients are 2 and 2, which are identical. These lines are parallel.

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