Formula of the slope of a linear function:
m = (y₂ - y₁)/(x₂ - x₁)
m= (-1 - 6)/[0- (-5)]
m= -7/5 This is the slope requested
Need additional information, which is the height and which is the diameter of the cylinder from the measurements supplied? Standard forumula for locating Radius and Volume of a cylinder are as follows.
Radius=Diameter/2

Volume=Base X height

Base= 3.14*r*r
The correct answer is -9/22.
The distance between a point

on the given plane and the point (0, 2, 4) is

but since

and

share critical points, we can instead consider the problem of optimizing

subject to

.
The Lagrangian is

with partial derivatives (set equal to 0)




Solve for

:


which gives the critical point

We can confirm that this is a minimum by checking the Hessian matrix of

:


is positive definite (we see its determinant and the determinants of its leading principal minors are positive), which indicates that there is a minimum at this critical point.
At this point, we get a distance from (0, 2, 4) of