# Question #f69d9

##### 1 Answer

#### Explanation:

This problem is asking us to find a line such that the line intersects the graph of

To do this, all we have to do is find the

Let's first solve for the

#y = (0)^3 + 4(0)^2 + 3(0) + 12#

#y = 12#

So the y intercept is

#(0) = x^3 + 4x^2 + 3x + 12#

We can group the terms in groups of two, and then factor and redistribute to get the following:

#0 = (x^3 + 4x^2) + (3x + 12)#

#0 = x^2(x + 4) + 3(x+4)#

#0 = (x^2+3)(x+4)#

Since these two terms multiplied together gives us zero, this means that either

#x+4 = 0#

#x = -4#

So our

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now, we have our two intercepts:

#m = (y_2-y_1)/(x_2-x_1) = (12 - 0)/(0 - (-4)) = 12/4 = 3#

So our slope is 3, and our

#y = 3x+12#

*Final Answer*