By definition, lines are parallel if they have the same slope.

The problem states that line A has a slope of  and that line X is parallel to it.

This means that line X must also have a slope of .

The y-intercept is not a determinant of lines being parallel or perpendicular.

If a line is parallel to another line, they will never intersect.  This means that their slopes will be the same.

The equation given is in standard form.  Convert the equation to slope intercept form, , in order to determine the slope .

Subtract  on both sides.

Simplify and reorganize the terms.

Divide by three on both sides.

Simplify both sides.

The slope of the parallel line must be .

To find the slope of a line parallel to any equation, the slopes will always be the same. We need to ensure we have  form.  stands for slope. In this case,  which is also our answer.

When finding the slope of a parallel line, we need to ensure we have  form. 

We need to solve for .

By adding  both sides and dividing  on both sides, we get    stands for slope.

Our  is   which is also the slope of the parallel line.

When finding the slope of a parallel line, we need to ensure we have  form. 

We need to solve for .

By subtracting  both sides and dividing  on both sides, we get 

Recall that  stands for slope.

Our  is  or  which is also the slope of the parallel line.

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, the slop is .  This is also the slope of the parallel line. 

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, we need to convert the equation into slope-intercept form.

Subtract  from both sides.

Divide both sides by .

Rewrite.

Identify the slope.

The slope is  or . This is also the slope of the parallel line.

When finding the slope of a parallel line, the slope will be the same as the other equation given. 

In order to determine the slope from an equation we need to make sure that it is written in the following format:

If the equation of a line is written in the slope-intercept form, then  is slope and  is the y-intercept.

In this case, we need to convert the equation into slope-intercept form.

Divide both sides by .

Identify the slope.

The slope is . This is also the slope of the parallel line.

Lines are parallel if they have the same slope. The lines are all given in the form y = mx + b. In this form, m represents the slope, thus, we are looking for another line with a slope of 2. This is y = 2x – 3. 

Note that the line given by y = (–1/2)x + 6 has a slope that is the negative reciprocal of 2. This line will be perpendicular to our given line.

When both equations are solved for the form  the slopes are the same.