Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = (negative one fourth)x + 8
–2x + 8y = 4
(1 point)
Responses
parallel
perpendicular
neither
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The given equation y = -(1/4)x + 8 is already in slope-intercept form y = mx + b, where m is the slope. In this case, the slope is -1/4.
To compare the slopes, we need to rewrite the second equation -2x + 8y = 4 in slope-intercept form. Solving for y, we get:
8y = 2x + 4
y = (2/8)x + (4/8)
y = (1/4)x + 1/2
Now we can compare the slopes: -1/4 and 1/4.
Since the slopes are negative reciprocals of each other (opposite signs and the absolute values are equal), the lines are perpendicular.
Therefore, the answer is perpendicular.