For the lines to be parallel, both the lines must have similar slopes.

Write the slope-intercept form.

The  represents the slope.  Both of the equation have a slope of negative three.  Therefore, both lines are parallel.

The answer is:  

If two lines are parallel, then they have the same slope.  To find the slope of a line, we write it in slope-intercept form

where m is the slope.  So given the equation

we must solve for y.  To do that, we will divide each term by 6.  We get

We can see the slope of this line is -7.  Therefore, this line is parallel to the line 

because it also has a slope of -7.

When looking at parallel lines, the slopes on both lines must be the same.  The y-intercept (or any other characteristic) of the lines do not matter. 

As long as the slopes are the same, the lines are parallel.

In order to determine whether if the lines are parallel, the lines must never intersect and share a similar slope to the equation given in the problem.

The equation is already in the form of:  

The variable  denotes the slope of the function.

The slope of the other line must be three to be parallel.  

The only possible answer is:  

the lines are parallel if both of the following conditions are met

•  is the same value for both equations
•  are different values in the two equations

For the lines

we see that the  values are not the same and as such

the lines are NOT parallel.

It is important to know that parallel lines have the same slope.

To see which line is parallel to the given equation you need to get all the lines in the form of , which means you need to get  by itself by bringing  to the other side.

Parallel lines have the same slope, so without needing to graph these equations, all we must do is identify the slope. Each of the equations is already in slope-intercept form, so we must only remember that the equation of a line is , where m represents the slope. Therefore, the parallel line is the one that also has a slope of 3--in this case, .

Point A is (5, 7). Point B is (x, y). The midpoint of AB is (17, –4). What is the value of B?

We need to use our generalized midpoint formula:

MP = ( (5 + x)/2, (7 + y)/2 )

Solve each separately:

(5 + x)/2 = 17 → 5 + x = 34 → x = 29

(7 + y)/2 = –4 → 7 + y = –8 → y = –15

Therefore, B is (29, –15).

A line's midpoint is the coordinate pair of that line which has the same number of points on either side of it. It bisects the line in two equal parts. 

Solution:

We are given that the line has an endpoint at  and its midpoint is on the origin. This known point would be in the Quadrant III and since on the opposite side of the midpoint there is exactly as much line we know that the other half of our line will lie in the Quadrant I. Add the absolute value of our known point to the coordinates of the origin to get . This is the unknown endpoint. You should recognize that this end point is exactly the same distance in the x and y direction (just opposite) as our given endpoint.