Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –4x + 3
–2x + 8y = 5
(1 point)
Responses
parallel
perpendicular
neither
To determine whether the lines are parallel, perpendicular, or neither, we need to examine the slope of each line.
For the first equation, y = -4x + 3, we can see that the slope is -4. This is because the equation is in the form y = mx + b, where m represents the slope. Therefore, the slope of the first equation is -4.
For the second equation, -2x + 8y = 5, we need to rewrite it in slope-intercept form (y = mx + b). So, we solve for y:
-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + (5/8)
From this form, we can see that the slope is 2/8, which simplifies to 1/4.
Now, we compare the slopes:
First equation: slope = -4
Second equation: slope = 1/4
Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
Therefore, the correct answer is neither.