# How do you identify equations as exponential growth, exponential decay, linear growth or linear decay 6x+5y=30?

May 28, 2015

Your equation is a linear equation. The variable $x$ is multiplied by a number only...no other operation is done on it.
You can check the "position" of $x$ to decide if is:
1] a linear (number)$\times$$x$;
2] e exponential (number)^(x);
Notice the difference in the "position" of $x$!!!
Have a look at this diagram:

In your case you have a linear [(number)$\times$$x$ = $6 x$] that can be written in $y = a x + b$ form as:
$y = - \frac{6}{5} x + 6$
So $a = - \frac{6}{5} < 0$ is a linear decay!

Hope it helps!