First, we need to find the slope of the above line. 

Given two points, , the slope can be calculated using the following formula:

Set :

Second, we note that the -intercept is the point . 

Therefore, in the slope-intercept form of a line, we can set  and :

There are two ways that you can find the y-intercept for an equation.  You could substitute  in for .  This would give you:

Simplifying, you get:

However, another way to do this is by finding the slope-intercept form of the line.  You do this by solving for :

Just divide everything by :

Remember that the slope-intercept form gives you the intercept as the final constant.  Hence, it is  as well!

There are two ways that you can find the y-intercept for an equation.  You could substitute  in for .  This would give you:

Simplifying, you get:

However, another way to do this is by finding the slope-intercept form of the line.  You do this by solving for .  Indeed, this is very, very easy.  Recall that the slope intercept form is:

This means that, as written, your equation obviously has .  You don't even have to do all of the simplification!

In order to figure this out, you should use your slope-intercept formula.  Remember that the y-intercept is the place where  is zero.  Therefore, the point  gives you your y-intercept.  It is .  Now, to find the slope, recall the slope equation, namely:

For your points, this would be:

This is your slope.

Now, recall that the point-slope form of an equation is:

, where  is your slope and  is your y-intercept

Thus, your equation will be:

In order to compute the slope of a line, there are several tools you can use.  For this question, try to use the slope-intercept form of a line.  Once you get the equation into this form, you basically can "read off" the slope right from the equation!  Recall that the slope-intercept form of an equation is:

Now, looking at each of your options, you know that you can eliminate two immediately, as their slopes obviously are not :

The next is almost as easy:

When you solve for , your coefficient value for  is definitely not equal to :

Next,  is not correct either.  When you start to solve, you should notice that  will always have a negative coefficient.  This means that it certainly will not become  when you finish out the simplification.

Thus, the correct answer is:

Really, all you have to pay attention to is the  term.  First, you will subtract  from both sides:

Then, just divide by , and you will have ! 

In order to rewrite the equation in slope-intercept form, we will need to multiply the reciprocal of the coefficient in front of y. 

Simplify both sides.

The answer is:

The slope-intercept form is:  

Subtract  on both sides.

Divide by negative six on both sides.

Simplify both sides.

The answer is:  

Slope intercept form is .

Add  on both sides.

Multiply by three on both sides.

The answer is:  

The slope-intercept form is defined as .

The equations in the answer choices are not in slope-intercept form.

The equation  is not linear.

The equation  is in standard form.

The answer is:  

The slope-intercept form is:  

Add  on both sides.

Simplify both sides of the equation.

The answer is: