I will first write the linear equation and then explain each part of it.

`z=6-2.3(x-6)+0.4(y-6)`

`z=-2,3x+0.4y+17.4`

Now to explain the equation in the first line (the second line is just simplified first line).

First part `6` is the initial value of `z.`

Second part `-2.3(x-6)` is there because each time `x` increases by `1,` `z` decreases by `2.3` and since the starting point for `x` is `6` we have `(x-6).`

Third part is the same as the second part the only difference is that instead of decreasing by `2.3,` `z` increases by `0.4,` hence `+0.4.`

Let's now check our equation.

First let's put in the initial state i.e. `x=6,y=6`

`z=6-2.3(6-6)+0.4(6-6)=6-0-0=6`

So we get `z=6` which is what we were supposed to get.

Let's check what happens if `x` increases from `6` to `7.`

`z=6-2.3(7-6)+0.4(6-6)=6-2.3=3.7`

So `z` is decreased by 2.3 which is what was supposed to happen.