The slope of a line in slope-intercept form is given by the coefficient,  in the equation:

. For two lines to be parallel, they have to have the same slope. Thus we see in our equation that  and so a line that is parallel must also have a slope of 

Parallel lines have equivalent slopes, so the correct answer is .

First write the equation in slope intercept form. Add  to both sides to get . Now divide both sides by  to get . The slope of this line is , so any line that also has a slope of  would be parallel to it. The correct answer is  .

Parallel lines will always have equal slopes. The slope can be found quickly by observing the equation in slope-intercept form and seeing which number falls in the "" spot in the linear equation , 

We are looking for an answer choice in which both equations have the same value. Both lines in the correct answer have a slope of 2, therefore they are parallel.

Lines are parallel when their slopes are the same.

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

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

Finding slope for these two lines is as easy as applying the slope formula to the points each line contains. We know that line  contains points  and , so we can apply our slope formula directly (pay attention to negative signs!)

.

Line  contains point  and, since the y-intercept is always on the vertical axis, . Thus:

The two lines have the same slope, , and are thus identical.

We are told at the beginning of this problem that line  is described by  . Since  is our slope-intecept form, we can see that  for this line. Since parallel lines have equal slopes, we must determine if line  has a slope of .

 Since we know that  passes through points  and , we can apply our slope formula:

Thus, the slope of line  is 1. As the two lines do not have equal slopes, the lines are not parallel.

Convert the equation to slope intercept form to get y = –1/3x + 2.  The old slope is –1/3 and the new slope is 3.  Perpendicular slopes must be opposite reciprocals of each other:  m_{1 *} m₂ = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

Convert the given equation to slope-intercept form.

The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is .

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

So the equation of the perpendicular line is .

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.