# Find the equation of the tangent to the curve #x + xy + y = 5# at #x = 5# help?

##### 2 Answers

#### Explanation:

Start by finding the y-value:

#5 + 5y + y = 5#

#6y = 0#

#y = 0#

Now we find the derivative using implicit differentiation.

#1 + y + x(dy/dx) + dy/dx = 0#

#y + x(dy/dx) + dy/dx = -1#

#x(dy/dx) + dy/dx = -1 - y#

#dy/dx(x + 1) = -1 - y#

#dy/dx = (-1 - y)/(x + 1)#

#dy/dx= -(y + 1)/(x + 1)#

At

#dy/dx= -1/6#

Now use point-slope form to find the equation:

#y - y_1 = m(x - x_1)#

#y - 0 = -1/6(x - 5)#

#y = -1/6x +5/6#

Hopefully this helps!

#### Explanation:

Begin by finding the y coordinate at

The point of tangency is

Compute the first derivative of the curve:

The slope, m, of the tangent line is the first derivative evaluated at the point

Use the point-slope form for the equation of a line:

Here is the a graph of the curve and the tangent line: