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.
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
1 answer