Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

Question

y = –4x + 3
–2x + 8y = 5
A. parallel
B. perpendicular.
C. neither

Answer 1

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

The first equation is in slope-intercept form (y = mx + b) where m is the slope. In this case, the slope is -4.

The second equation can be rearranged to slope-intercept form by solving for y. Subtracting -2x from both sides gives 8y = 2x + 5. Dividing through by 8 gives y = (2/8)x + 5/8. Simplifying further gives y = (1/4)x + (5/8). Therefore, the slope of the second equation is 1/4.

Since the slopes of the two equations (m₁ = -4 and m₂ = 1/4) are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Therefore, the correct answer is C. neither.