Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
y = –4x + 3
–2x + 8y = 5
(1 point)
Responses
parallel
parallel
perpendicular
perpendicular
neither
neither
neither
y = –4x + 3 m so slope = m1 = -4
–2x + 8y = 5
or 8 y = 2 x + 5
or y = 1/4 x + 5/8 so slope = m2 = 1/4
\NOW we see that m2 = -1/m1
If you draw those two slopes you will notice they are PERPENDICULAR
which is very likely if m2 = -1/m1
perpendicular
To determine whether the lines are parallel, perpendicular, or neither, we need to compare the slopes of the two equations.
First, let's rewrite the second equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
-2x + 8y = 5
8y = 2x + 5
y = (2/8)x + (5/8)
y = (1/4)x + (5/8)
Comparing the equations, we can see that the slope of the first equation is -4, while the slope of the second equation is 1/4.
If two lines are parallel, their slopes are equal. Since -4 is not equal to 1/4, we can conclude that the lines are not parallel.
If two lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of 1/4 is -4. Therefore, the slopes of the two lines are negative reciprocals, indicating that the lines are perpendicular.
Hence, the correct answer is:
perpendicular