The slope of a line perpendicular to the given line is -2.
The slope of a line parallel to the given line is 1/2.
To find the slopes of lines perpendicular and parallel to the given line, we first need to rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Given equation: 4x - 8y = 5
Rearrange the equation to solve for y:
-8y = -4x + 5
y = (1/2)x - (5/8)
Now that the equation is in slope-intercept form, we can identify the slope of the given line:
m1 = 1/2
For a line to be parallel to the given line, it must have the same slope. So, the slope of a line parallel to this line is:
m_parallel = 1/2
For a line to be perpendicular to the given line, its slope must be the negative reciprocal of the slope of the given line. So, the slope of a line perpendicular to this line is:
m_perpendicular = -1/m1 = -1/(1/2) = -2