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
Neither
To determine whether the graphs of the given equations are parallel, perpendicular, or neither, we need to compare their slopes.
The first equation, y = 4x - 2, is in slope-intercept form y = mx + b, where m is the slope. The slope of this equation is 4.
The second equation, -x + 4y = 0, can be rewritten in slope-intercept form by solving for y. Adding x to both sides and dividing by 4, we get y = (1/4)x. The slope of this equation is 1/4.
Since the slopes of the two equations are different (4 and 1/4), the graphs of the equations are neither parallel nor perpendicular.