There are 2 tangent lines that pass through the point

and

Explanation:
Given:

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:
![[1]](https://tex.z-dn.net/?f=%5B1%5D)
For the lines to be tangent to the curve, we must substitute the first derivative of the curve for
:



![[2]](https://tex.z-dn.net/?f=%5B2%5D)
Substitute equation [2] into equation [1]:
![[1.1]](https://tex.z-dn.net/?f=%5B1.1%5D)
Because the line must touch the curve, we may substitute 

Solve for x:




± 
±
<em> </em>

There are 2 tangent lines.

and

Let's solve for y.
4x+7y=28
Add -4x to both sides.
4x+7y+−4x=28+−4x
7y=−4x+28
Divide both sides by 7.
7y/7=−4x+28/7
y=−4/7x+4
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