Can someone me out real quick? consider the line x+6y=-1 what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line?

The slope of a line perpendicular to this line would be 6. The slope of a line parallel to this would be -1/6.

To find these, you first have to solve for slope-intercept form.

x + 6y = -1 > subtract x from both sides

6y = -x - 1 > divide both sides by 6

y = -1/6x - 1/6

Now we know the original slope to be -1/6. Since that is the case, we can find the parallel line to be the same since parallel lines have the same slope.

We also know that perpendicular lines have opposite and reciprocal slopes from the originals. So we flip it and make it positive to get 6.