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
To determine whether the lines are parallel or perpendicular, we need to compare their slopes.
For the first equation, y = -4x + 3, the slope is -4.
To find the slope of the second equation, we need to rewrite it in slope-intercept form (y = mx + b).
-2x + 8y = 5
Rewriting the equation, we get 8y = 2x + 5
Dividing by 8, we have y = (2/8)x + 5/8
Simplifying, we get y = (1/4)x + 5/8
The slope of the second equation is 1/4.
Since the slopes are not equal, the lines are not parallel.
To determine whether they are perpendicular, we need to check if the product of their slopes is -1.
The product of -4 and 1/4 is -1/4.
Since the product of the slopes is not -1, the lines are not perpendicular.
Therefore, the lines for this pair of equations are neither parallel nor perpendicular. Thus, the answer is C. neither.