tell whether the lines for each pair of equations are parallel, perpendicular, or neither
y =-1/4x + 10
-2x + 8y = 6
To determine whether the lines are parallel, perpendicular, or neither, we can compare the slopes of the lines.
The given pair of equations are:
1) y = -1/4x + 10
2) -2x + 8y = 6
Let's rewrite the second equation in slope-intercept form (y = mx + b):
-2x + 8y = 6
8y = 2x + 6
y = 2/8x + 6/8
y = 1/4x + 3/4
Now we can compare the slopes of the two lines:
1) The slope of the first line is -1/4.
2) The slope of the second line is 1/4.
Since the slopes are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1.
(-1/4) * (1/4) = -1/16
Since the product of the slopes is not -1, the lines are not perpendicular.
Therefore, the lines are neither parallel nor perpendicular.