Determine whether the graphs of the given equation are parallel, perpendicular, or neither. Explain
y=4x-2
-X+4y=0
y = 4x - 2 ----> slope is 4
-x + 4y = 0
4y = x
y = (1/4)x --- slope is 1/4
lines are not parallel, nor perpendicular
To determine whether the graphs of the two equations are parallel, perpendicular, or neither, we need to compare their slopes.
The given equation, y = 4x - 2, is already in slope-intercept form (y = mx + b), where the coefficient of x is the slope. In this case, the slope is 4.
Now let's rearrange the second equation, -X + 4y = 0, in slope-intercept form:
-4y = x
y = -(1/4)x
Comparing the slopes of the two equations, we see that the slope of the first equation is 4, and the slope of the second equation is -(1/4).
If two lines are parallel, their slopes are equal. If two lines are perpendicular, their slopes are negative reciprocals of each other. If neither of these conditions is met, the lines are neither parallel nor perpendicular.
In this case, the slope of the first equation, 4, is not equal to the slope of the second equation, -(1/4). Therefore, the graphs of the given equations are neither parallel nor perpendicular.