The slope-intercept form of a line is represented as:

To rearrange  into  form, we must get  by itself.

1)  (add  to and subtract  from both sides)

2) 

3)  (divide both sides by )

4) 

Recall that our slope-intercept form is 

First, we get the  term by itself:

  (subtract  from both sides)

Then:

 (multiply both sides by the reciprocal of the  coefficient)

Our answer is 

You may know that parallel lines have the same slope. With that in mind, it may be tempting to see that  there and find an equation with  and a different y-intercept.

Be careful of that trap! Notice that equation is written in STANDARD form, and to find the slope of a line we must get it into slope-intercept form, 

Arranging the equation  into slope-intercept form, we see that we get 

Our slope is , so a line parallel could be , one of our choices.

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.