Recall that perpendicular lines have slopes that are negative reciprocals.

Start by putting  into slope-intercept form.

The slope of the given line is , which means that the line perpendicular to it must have a slope of .

 is the only line that has the required slope.

Recall that parallel lines have the same slope. Start by putting the given equation of a line in slope-intercept form.

Since the given line has a slope of , a line parallel to it must also have the same slope. Thus,  is parallel to the given line.

A line perpendicular to a given line has as its slope the opposite of the reciprocal of the slope of the first line. The given line has slope 

.

The opposite of the reciprocal of this can be obtained by switching numerator and denominator, then changing sign. The number is , the slope of the line in question. This is the correct choice.

Two lines on the coordinate plane are parallel if and only if they have the same slope. Since Line  is parallel to Line , and Line  has slope , Line  also has slope .

Identify the slope of the line perpendicular to the given linear equation.

Perpendicular lines intersect at 90 degree angles. To find the slope of a line perpendicular to another known line, we need to take find the opposite reciprocal of our known slope. 

The reciprocal of a fraction is simply what we get when we flip a fraction.

Thus, we get:

All we did was exchange our numerator.

However, we also need "the opposite" this means that we also change the sign of our slope.

So, our new slope is

Start by putting the given line in slope-intercept form.

Recall that parallel lines have the same slope.

Thus,  must be parallel to the given line.

Start by putting the given equation of a line into slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. Thus,  is the only line that has a slope that is the negative reciprocal of .

Which of the following lines is perpendicular to the following function?

Perpendicular lines have opposite reciprocal slopes. 

What is the slope of our given equation? To find this, we need to move the negative four over to the right hand side of the equation.

So, our original slope is -1

The opposite reciprocal of -1 is 1

So our answer must have a slope of 1

Start by re-arranging the given equation into slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. This means that the line that is perpendicular to the given one has a slope of .

 is the only line with that slope.

If the slope of a line is given, the slope of a line perpendicular to it is the additive inverse of the reciprocal of the slope of the first line. Thus, the slope sought is 

.