Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y equals 4 x minus 2.
negative x plus 4 y equals 0.
(1 point)
Responses
Parallel
Parallel
Perpendicular
Perpendicular
Neither
To determine whether the graphs of the given equations are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
The equation y = 4x - 2 is in slope-intercept form (y = mx + b), where the coefficient of x (m) represents the slope. In this case, the slope is 4.
The equation -x + 4y = 0 can be rewritten as 4y = x, or y = (1/4)x. Again, the coefficient of x represents the slope, which is 1/4.
Since the slopes of the two lines are different (4 and 1/4), the graphs of these equations are perpendicular.