Start by converting the original equation to slop-intercept form.

The slope of this line is . A parallel line will have the same slope. Now that we know the slope of our new line, we can use slope-intercept form and the given point to solve for the y-intercept.

Plug the y-intercept into the slope-intercept equation to get the final answer.

The line parallel to must have a slope of , giving us the equation . To solve for b, we can substitute the values for y and x.

Therefore, the equation of the line is .

Converting the given line to slope-intercept form we get the following equation:

For parallel lines, the slopes must be equal, so the slope of the new line must also be . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line.

Use the y-intercept in the slope-intercept equation to find the final answer.

Find the slope of the given line:  (slope intercept form)

 therefore the slope is 

Parallel lines have the same slope, so now we need to find the equation of a line with slope  and going through point  by substituting values into the point-slope formula.

So, 

Thus, the new equation is 

This is a two-step problem. First, the slope of the original line needs to be found. The slope will be represented by "" when the line is in -intercept form .

So the slope of the original line is . A line with perpendicular slope will have a slope that is the inverse reciprocal of the original. So in this case, the slope would be . The second step is finding which line will give you that slope. For the correct answer, we find the following:

So, the slope is , and this line is perpendicular to the original.

Since parallel lines have equal slopes, you should find the slope of the line given to you. The easiest way to do this is to solve the equation so that its form is .   represents the slope.

Take your equation: 

First, subract  from both sides:

Next, subtract  from both sides:

Finally, divide by :

, which is the same as 

Thus, your slope is .

Among the options provided only  is parallel. Solve this equation as well for  form.  

First, subtract  from both sides:

Then, divide by :

Parallel lines have the same slope but different y-intercepts. When the equations of two lines are the same they have infinitely many points in common, whereas parallel lines have no points in common.

Our equation is given in slope-intercept form,

where  is the slope. In this particular situation .

Therefore we want to find an equation that has the same  value and a different  value.

Thus,

 is parallel to our equation.

Parallel lines have the same slope and differing y-intercepts. Since  is the only equation with the same slope, and the y-intercept is different, this is the equation of the parallel line.

Parallel lines have the same slope and different y-intercepts. If their y-intercepts and slopes are the same they are the same line, and therefore not parallel. Thus the only one that fits the description is:

The first step in solving for a parallel line is to find the slope of the original line. In this case, .

Our new line has an equal slope (the definition of parallel) and passes through , so substituting into our slope-intercept equation gives us:

 --->  ---> .

Thus, the slope intercept equation for our parallel line is .