Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y=-1/4x+10
-2x+8y=6
(1 point)
A. parallel
B. perpendicular
C. neither
To determine whether two lines are parallel or perpendicular, we need to compare their slopes.
First, let's rewrite both equations in slope-intercept form, which is y = mx + b:
The equation y = -1/4x + 10 is already in slope-intercept form with a slope (m) of -1/4.
To rewrite the second equation, -2x + 8y = 6, into slope-intercept form, we need to isolate y by adding 2x to both sides and then dividing the whole equation by 8:
8y = 2x + 6
y = 1/4x + 3/4
So the second equation is y = 1/4x + 3/4, which has a slope (m) of 1/4.
Comparing the slopes, we see that the slopes of the two lines are negative reciprocals of each other: -1/4 and 1/4.
Since the slopes of the two lines are negative reciprocals, the two lines are perpendicular to each other.
Therefore, the answer is B. perpendicular.