Are the following lines parallel, perpendicular, or neither?
x-6y=12
6x+y=6
i think it is neither
The slope of your first line is 1/6,
the slope of the second is -6
their product is -1, so the two lines are perpendicular.
To determine whether the given lines are parallel, perpendicular, or neither, we need to analyze their slopes.
The equations of the lines can be rewritten in slope-intercept form (y = mx + b), where "m" represents the slope:
x - 6y = 12
can be rearranged as:
-6y = -x + 12
y = (1/6)x - 2
6x + y = 6
can be rearranged as:
y = -6x + 6
Now we can compare the slopes of the two lines:
The slope of the first line is 1/6.
The slope of the second line is -6.
Two lines are parallel if and only if their slopes are equal. Since 1/6 is not equal to -6, the given lines are not parallel.
Two lines are perpendicular if and only if the product of their slopes is -1. Let's check if the product of these slopes is -1:
(1/6) * (-6) = -1
The product is -1, which means the slopes are negative reciprocals of each other. Therefore, the given lines are perpendicular.
In summary:
The given lines are perpendicular to each other.