Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y=-4x+3
-2x+8y=5
Answers:
parallel
perpendicular
neither

Answer 1

To determine if the lines are parallel, perpendicular, or neither, we need to check the slopes of the equations.

For the first equation y = -4x + 3, the slope is -4.

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

-2x + 8y = 5
8y = 2x + 5
y = 0.25x + 0.625

The slope of the second equation is 0.25.

Since the slopes are not the negative reciprocals of each other (i.e., not equal to -1), the lines are neither parallel nor perpendicular.