A plane has equation

z $3=0\mathrm{.}2($x $2)+0\mathrm{.}4($y $4).$

The point

$($x$,$ y$,$ z$)=(2,4,3)$

lies on this plane.

$($a$)$ By how much does z increase if x is increased by one? $($Give an exact answer.$)$

$($b$)$ By how much does z increase if y is increased by one? $($Give an exact answer.$)$

$($c$)$ By how much does z increase if x is increased by $6$ and y is increased by $7?($Give an exact answer.$)$