Consider the line -4x-8y=6.

What is the slope of a line parallel to this line?

What is the slope of a line perpendicular to this line?

rewrite as

8y = -4x+6
y = -1/2 x + 3/4

so, y and all parallel lines have slope m = -1/2

all perpendicular lines have slope -1/m = -1/(-1/2) = +2

To find the slope of a line parallel to the given line, we need to determine the slope of the given line. The given line is in the form of standard equation Ax + By = C, where A, B, and C are constants. In this case, the given line is -4x - 8y = 6.

Step 1: Convert the equation to slope-intercept form, y = mx + b, by solving for y.
-4x - 8y = 6
-8y = 4x + 6
y = (4/8)x + (6/-8)
y = (1/2)x - 3/4

The slope of the given line, m1, is 1/2.

To find the slope of a line parallel to the given line, we can use the fact that parallel lines have the same slope. Therefore, the slope of a line parallel to -4x - 8y = 6 is also 1/2.

To find the slope of a line perpendicular to the given line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 1/2 is -2. Therefore, the slope of a line perpendicular to -4x - 8y = 6 is -2.

To find the slope of a line, we need to rearrange the equation into slope-intercept form (y = mx + b), where "m" represents the slope.

Given the equation -4x - 8y = 6, let's rearrange it:
-8y = 4x + 6
To isolate the variable y, we can divide both sides of the equation by -8:
y = (-1/8)x - 3/4

Now that the equation is in slope-intercept form, we see that the slope of the given line is -1/8.

To find the slope of a line parallel to the given line, we know that parallel lines have the same slope. Therefore, any line parallel to -4x - 8y = 6 will also have a slope of -1/8.

To find the slope of a line perpendicular to the given line, we use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The negative reciprocal of -1/8 is 8/1, simplified to 8. Therefore, a line perpendicular to -4x - 8y = 6 will have a slope of 8.