The student was correct in the attempt to get the equation into slope-intercept form,  by dividing by  on both sides.

The slope should have been: 

The y-intercept was correct in being: 

Start by finding the slope of the line.

Recall how to find the slope:

Using the given points,

Now, we can write the equation for the line as the following:

, where  is the y-intercept that we still need to find.

Take one of the points and plug it into the equation for  and , then solve for .

Using the point ,

Thus, the equation of the line must be 

So our final answer should appear in slope-intercept form,  with  representing the slope and  representing the y-intercept. We know that our slope is , meaning . 

Now we have  but we still need to find our y-intercept, . 

To solve for the y-intercept, we'll need to use the coordinates given to us in the question to replace the  and . Remember that in a coordinate the  is our first number and our  is the second number, like so: .

Since we are working with fractions here i'll show how to solve this without a calculator, but using one will make it quicker.

Replace the  and y with  and  respectively and then solve as if you solving for , but with .

Since we are multiplying with a fraction, our  can be changed to look like , which is 's fraction form. Multiply across both the top and bottom.

So now we have this:

Subtract the  on both sides, and since we're subtracting by a fraction we'll need our  to become a fraction too. We can't use  because for adding and subtracting our denominators must be the same, so I will multiply  with  in order to get the same denominator. 

Now that our  has become  (it's still , despite how big the fraction looks.) we can use it with our subtraction of . Subtract only the numerator though, not the denominator.

Now that we have our y-intercept, we can take out the  and  and replace our  with .

Our answer should be in slope-intercept form,  with  representing our slope and  representing our y-intercept. We know that our slope is, which means . 

This should give us , but we still need to find our y-intercept; .

In order to find our y-intercept, we'll need to replace our  and  with those of our coordinates in the question. Remember that in a coordinate the first number is our  while our second number is , as shown here: .

Replace  and  with that of  and  and then solve the problem as if you were solving for , but with .

Both negatives when multiplied cancel to create a positive:

Subtract  from both sides:

Our y-intercept is , so now we can take out the  and  and replace the  with .

So we know we need this problem to end as a slope-intercept formula,  with  representing our slope and  representing our y-intercept.

From the question we know that our slope is , which means . So we have  so far, now we need to find our y-intercept; .

To find , you need to plug in our coordinates  into the equation. Remember that the first number of a coordinate is your , and the second one is your , like this .

Take the  and  of the coordinate and substitute them for your  and , so you should end up with something looking like this: 

Solve the problem from there like you would to find , only with .

Our y-intercept is , so now we can take out the  and  and substitute the  for . 

The slope-intercept form of the equation of a line is 

for some constant .

To rewrite 

in this form, it is necessary to solve for , isolating it on the left-side. First, add  to both sides:

Multiply both sides by :

Distribute on the right:

This is the correct choice.

Recall what the slope intercept form is:

You will need to algebraically rearrange the given equation.

 is the slope-intercept form of the equation given in standard form.

Recall our point-slope form

Here  and  and 

So, plugging those in gives us

Lets distribute that 2

and add 4 to both sides

And simplify