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.