Question

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

y = -7/4x – 1
16x – 28y = –32

Answer 1

The lines represented by the equations y = -7/4x - 1 and 6x - 28y = -32 are neither parallel nor perpendicular, as their slopes -7/4 and 3/14 are neither equal nor negative reciprocals.

Step-by-step explanation:

The question asks whether the lines represented by each pair of equations are parallel, perpendicular, or neither. To determine this, we compare the slopes of the lines since parallel lines have the same slope while perpendicular lines have slopes that are negative reciprocals of each other.

The first equation is y = -7/4x - 1. The slope here is -7/4. For the second equation, 6x - 28y = -32, we can rewrite it in slope-intercept form (y = mx + b) by dividing every term by -28, which gives us y = (6/28)x + (32/28) or y = 3/14x + 8/7. The slope in this case is 3/14.

Since the slopes -7/4 and 3/14 are neither equal nor negative reciprocals of each other, the two lines are neither parallel nor perpendicular.