Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –4x + 3
–2x + 8y = 5
A. parallel
B. perpendicular
C. neither

Answer 1

To determine whether the lines are parallel, perpendicular, or neither, we need to compare their slopes.

The given equation y = -4x + 3 is in slope-intercept form, y = mx + b, where m is the slope. So, the slope of this line is -4.

To find the slope of the second equation -2x + 8y = 5, we need to rearrange it into slope-intercept form.

-2x + 8y = 5
8y = 2x + 5
y = 2/8x + 5/8
y = 1/4x + 5/8

From this equation, we can see that the slope is 1/4.

Since the slopes of the two lines are not equal or negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Therefore, the answer is C. neither.