Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –1/4x + 10
–2x + 8y = 6
(1 point)
Responses
parallel
parallel
perpendicular
perpendicular
neither
To determine whether two lines are parallel or perpendicular, we need to compare their slopes.
For the first pair of equations:
y = -1/4x + 10
The slope of this line is -1/4.
For the second equation:
-2x + 8y = 6
To put this equation in slope-intercept form (y = mx + b), we need to solve for y:
8y = 2x + 6
y = (2/8)x + (6/8)
y = 1/4x + 3/4
The slope of this line is 1/4.
Since the slopes of the two lines are not equal and not negative reciprocals, they are neither parallel nor perpendicular.