Question

for each of the following equations, determine whether y is a function of x.

$x + 4y = 8$	$circ$ function $circ$ not a function
$x = 5y^2 - 3$	$circ$ function $circ$ not a function
$y = 7x$	$circ$ function $circ$ not a function
$x = -9y$	$circ$ function $circ$ not a function

Explanation:

Step1: Rewrite to solve for y

$x + 4y = 8 \implies y = \frac{8 - x}{4}$
Each $x$ has one $y$ value.

Step2: Rewrite to solve for y

$x = 5y^2 - 3 \implies y^2 = \frac{x + 3}{5} \implies y = \pm\sqrt{\frac{x + 3}{5}}$
One $x$ has two $y$ values.

Step3: Check given y in terms of x

$y = 7x$
Each $x$ has one $y$ value.

Step4: Rewrite to solve for y

$x = -9y \implies y = -\frac{x}{9}$
Each $x$ has one $y$ value.

Answer:

1. $x + 4y = 8$: Function
2. $x = 5y^2 - 3$: Not a function
3. $y = 7x$: Function
4. $x = -9y$: Function