The easiest way to determine the slope and y-intercept of a line is by rearranging its equation to the form. In this form, the slope is the  and the y-intercept is the .

Rearranging

gives you

which has an of 2 and a of 6.

When finding the equation of a line given two or more points, the first step is to find the slope of that line. We can use the slope equation, . Any combination of the three points can be used, but let's consider the first two points,  and .

So  is our slope.

Now, we have the half-finished equation

and we can complete it by plugging in the  and  values of any point. Let's use .

Solving

for  gives us

so

We now have our completed equation: 

We need to find the equation of the line in slope-intercept form.

In this formula, is equal to the slope and is equal to the y-intercept.

To find this equation, first, we need to find the slope by using the formula for the slope between two point.

In the formula, the points are  and .  In our case, the points are  and . Using our values allows us to solve for the slope.

We can replace the variable with our new slope.

Next, we need to find the y-intercept. To find this intercept, we can pick one of our given points and use it in the formula.

Solve for .

Now, the final equation connecting the two points can be written using the new value for the y-intercept.

Since all of the answers are in the  form, the slope of each line is indicated by its  and its y-intercept is indicated by its . Thus, a line with a slope of  and a y-intercept of  must have an equation of .

The expression under the radical must be .  Hence

Solving for , we get

First, use the slope formula to find the slope, setting .

We can write the equation in slope-intercept form as

.

Replace :

We can find  by substituting for  using either point - we will choose :

The equation is .

First, use the slope formula to find the slope, setting .

We can write the equation in slope-intercept form as

.

Replace :

We can find  by substituting for  using either point - we will choose :

The equation is .

To find the equation of a line, we need to know the slope and a point that passes through the line.  We can then use the equation  where m is the slope of the line, and  a point on the line.  For parallel lines, the slopes are the same.  The slope of  is 3, so the slope of the parallel line will be 3 as well.  We know that the parallel line needs to contain the point (0,1), so we have all of the information we need.  We can now use the equation 

The equation of a line is written in the following format: 

1) The first step, then, is to find the slope, .

 is equal to the change in  divided by the change in .

So,

2) Next step is to find . We can find values for  and  from any one of the given points, plug them in, and solve for .

Let's use (4,3)

So, 

Then we just fill in our value for , and we have  as a function of .

When an equation is in the  form, its slope is  and its y-intercept is . Thus, we need an equation with an  of 4 and a  of 6, which would be