Ordinarily, we would use point-slope form, , to construct a proper parallel from a point and a slope. However, in this case, we have been given a y-intercept by the problem itself, so sticking with slope-intercept form is easiest.

If the new line passes through , then we know the y-intercept is . Since slope is equal in parallel lines, and the slope of our comparison line is , we know the slope of our new line is .

Thus, .

The correct answer is,  .

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Subtract  from both sides of the equation.

Simplify.

Divide both sides of the equation by .

Simplify.

Reduce.

Because the given line has the slope of , the line parallel to it must also have the same slope.

Since the lines are parallel, the slopes must be the same. Therefore, (p+3) divided by (–2–5) must equal –2. 11 is the only choice that makes that equation true. This can be solved by setting up the equation and solving for p, or by plugging in the other answer choices for p. 

First, put the equation in slope-intercept form: y = 3x + 6. From there we can see the slope of this line is 3 and since the slope of any line parallel to another line is the same, the slope will also be 3.

This problem requires an understanding of the makeup of an equation of a line.  This problem gives an equation of a line in y = mx + b form, but we will need to algebraically manipulate the equation to determine its slope.  Once we have determined the slope of the line given we can determine the slope of any line parallel to it, becasue parallel lines have identical slopes.  By dividing both sides of the equation by 5, we are able to obtain an equation for this line that is in a more recognizable y = mx + b form. The equation of the line then becomes y = 6/5x + 12/5, we can see that the slope of this line is 6/5.  

We rearrange the line to express it in slope intercept form.

Any line parallel to this original line will have the same slope.

Parallel lines will have equal slopes. To solve, we simply need to rearrange the given equation into slope-intercept form to find its slope.

The slope of the given line is . Any lines that run parallel to the given line will also have a slope of .

Parallel lines have the same slope. The question requires you to find the slope of the given function. The best way to do this is to put the equation in slope-intercept form (y = mx + b) by solving for y.

First subtract 6x on both sides to get 3y = –6x + 12.

Then divide each term by 3 to get y = –2x + 4.

In the form y = mx + b, m represents the slope. So the coefficient of the x term is the slope, and –2 is the correct answer. 

To answer this question, we must find the slope of a line parallel to the line .

When a line is parallel to another, they have the same slope. Therefore, if we find the slope of the line we are given, we will find the slope of any line that would be parallel to it. 

To find the slope, we must put our equation into point-intercept form. Point-intercept form is displayed as the following:

, where  is the slope and  is where the line intercepts the -axis.

Note that to put a line into point-intercept form, you must solve for .

Therefore, we must solve for . So, for this data, we must first subtract both sides of the equation by :

This becomes:

Now we must divide each side by  to get  by itself:

This becomes:

Because  is  in our point-intercept form, the slope of our line is . Therefore, the slope of any line parallel to this line is also .

Parallel lines have the same slope. You find slope by using the general form of slope-intercept:

where  represents the slope of the line and  represents the -intercept.

For our equation we see that the 

 is 

thus the anser is .