Two lines are perpendicular if their slopes have opposite signs (positive/negative) and they are reciprocals of each other.

To find a reciprocal of a number, we will write it in fraction form. Then, the numerator becomes the denominator and the denominator becomes the numerator. In other words, we flip the fraction.

We will look at the lines in slope-intercept form

where m is the slope and b is the y-intercept.

So, given the equation

we can see the slope is . Now, the opposite reciprocal of this slope is  which is the same as . So, we will find the equation that has  as the slope.

So, in the equation

we can see the slope is . Therefore, it is perpendicular to the original equation.

Two lines are parallel if they have the same slope. So, we will look at the lines in slope-intercept form:

where m is the slope and b is the y-intercept.

So, given the line

we can see the slope is -2. So, to find a line that is parallel, it must also have a slope of -2. So, the line

we can see it also has a slope of -2. Therefore, it is parallel to the original line.

The perpendicular line slope will be the negative reciprocal of the original slope.

Substitute the given slope into the equation.

The answer is:  

The slope of the perpendicular line is the negative reciprocal of the original slope.

Substitute the slope into the equation.

The answer is:  

When lines are parallel, their slopes are equal.

Rewrite the given equation in standard form to slope-intercept form:

Subtract  from both sides.

Divide by negative seven on both sides.

The equation becomes:  

The answer is:  

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

The slope of the given line is .

Next, recall that the slope of perpendicular lines are negative reciprocals. To get the negative reciprocal, change the sign of the given slope and flip the numerator and denominator.

The negative reciprocal of  is .

The equation of the line is the slope is in slope-intercept form:  

The slope is three.

The perpendicular line is the negative reciprocal of the original slope.

Substitute the slope into the equation.

The answer is:  

Start by placing the given equation in slope-intercept form.

Recall that parallel lines must have the same slope. Thus,  is the only line that is parallel to the given one.

Start by rewriting the equation in slope-intercept form.

Recall that perpendicular lines have slopes that are negative reciprocals of each other. To find the negative reciprocal, flip the signs, and switch the numerator and denominator around. 

The negative reciprocal of  is . Thus, the line perpendicular to the given one must be .

Which of the following lines is parallel to ?

For two lines to be parallel, they must be equidistant at all points and never cross. This will only happen if the two lines have equal slope.

Recall that slope is the number in front of the x. In this case, it is negative 4

So, the only option with slope of negative 4 is:

Don't be fooled by any of the similar looking options!