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Determine whether the pair of lines is parallel perpendicular or neither

3x - 6y = -4
18x + 9y = -10

User Bhinks
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Final answer:

After converting both equations to slope-intercept form, we determined that the slopes of the lines represented by the equations 3x - 6y = -4 and 18x + 9y = -10 are 1/2 and -2, respectively. Since the product of their slopes is -1, the lines are perpendicular to each other.

Step-by-step explanation:

To determine whether the pair of lines represented by the equations 3x - 6y = -4 and 18x + 9y = -10 are parallel, perpendicular, or neither, we need to find the slopes of these lines. To do this, we can rearrange each equation into slope-intercept form (y = mx + b), where m represents the slope.

The first equation can be transformed as follows:

  • 3x - 6y = -4
  • -6y = -3x - 4
  • y = (⅔)x + (⅓)


So, the slope of the first line, m1, is ⅔ (or 0.5).

Following the same process for the second equation:

  • 18x + 9y = -10
  • 9y = -18x - 10
  • y = (-2)x + (-⅖)


This gives us the slope of the second line, m2, as -2.

Two lines are parallel if their slopes are equal, perpendicular if the product of their slopes is -1, and neither if the lines don't meet either of these criteria. Since m1 (⅔) and m2 (-2) satisfy the relationship m1 × m2 = -1, we conclude that the lines are perpendicular to each other.

User Nambrot
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