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!

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 .