INSTRUCTOR: Find dy dx if y is defined implicitly as a function of x by the equation x squared plus xy minus y squared plus 7x minus 3y minus 26 equals 0. What is the equation of the tangent line to the graph of this curve at the point 3 comma negative 2?

We're going to use the fact that dy dx is equal to negative fx divided by fy. We're going to use that fact. So let's first find fx for this equation. That will be equal to 2x plus y plus 7. And fy is equal to x minus 2y minus 3.

Evaluating-- well, actually let's not evaluate that yet. Let's go ahead and just say what dy dx is. So this means that dy dx is equal to negative a fraction with a numerator of 2x plus y plus 7 and a denominator of x minus 2y minus 3.

Now we can evaluate dy dx at the point 3 negative 2. And that will be negative 11 over 4. So that is the slope of our tangent line. We have the point 3, negative 2. So we'll use our point slope form.

So we'll have y minus y1 equals m parentheses x minus x1, close parentheses, with the point 3 negative 2 is our x1 y1 and our slope as negative 11 fourths. So this will be y plus 2 equals negative 11 over 4, open parenthesis, x minus 3.

Distributing and solving for y, we see that y is equal to negative 11 over 4x plus 25 over 4. And that is the equation of the tangent line at that point.