The given equation will need to be rewritten in slope intercept format.

Divide by two on both sides.

Rearrange the right side by order of powers.

The slope can be seen as 

The answer is:  

The slope in a linear equation is defined as .

The x-variable exists in the denominator, which refers to the parent function of:

This function is not linear, and will have changing slope along its domain.

The answer is:  

The equation of a parabola can be written in vertex form

where  is the vertex and  determines if it is a minimum or maximum. If is positive, then it is a minimum; if is negative, then it is a maximum.

In this example, is negative, so the vertex is a maximum.

and

Rewrite the equation by the order of powers.

This is a parabola in standard form:  

Determine the values of  to the vertex formula.

Since the leading coefficient of the parabola is negative, the parabola will curve downward and will have a maximum point.  

Therefore there is a maximum at,

 .

First, subtract 7 to both sides.

Factor the y on the left hand side.

Divide both sides by 3 – x.

Take an extra step by factoring the minus sign on the denominator.

Cancel the minus signs.

Let .

First, calculate the slope between the two points.

Next, use the slope-intercept form to calculate the intercept. We are able to plug in our value for the slope, as well the the values for .

Using slope-intercept form, where we know and , we can see that the equation for this line is .

To calculate a line passing through two points, we first need to calculate the slope, .

Now that we have the slope, we can plug it into our equation for a line in slope intercept form.

To solve for , we can plug in one of the points we were given. For the sake of this example, let's use , but realize either point will give use the same answer.

Now that we have solved for b, we can plug that into our slope intercept form and produce and the answer

We are looking for a point, , where these two lines intersect. While there are many ways to solve for and given two equations, the simplest way I see is to use the elimination method since by adding the two equations together, we can eliminate the variable.

Dividing both sides by 7, we isolate y.

Now, we can plug y back into either equation and solve for x.

Next, we can solve for x.

Therefore, the point where these two lines intersect is .

The first thing is to plug in the given value so you equation is 

.  

Then you must subtract  from both sides in order to get  by itself.  

You now have 

and you must multiply by  for each side and you get .

Add  on both sides.

Subtract 2 from both sides.

Divide by 10 on both sides.

Reduce the fractions.

The answer is: