Question

identify examples and non - examples of the standard form of a linear function.
$5x - 3y = 9$
$y = \frac{5}{6}x - 3$
$2x + 3y = 0$
$x + y = 1$
$x = 6y$
$y = x - 2$
examples
non - examples

Explanation:

Step1: Recall standard linear form

The standard form of a linear function is $Ax + By = C$, where $A$, $B$, and $C$ are constants, and $A$, $B$ are not both 0.

Step2: Classify each equation

• $5x - 3y = 9$: Matches $Ax+By=C$ → Example
• $y = \frac{1}{6}x - 3$: Slope-intercept form → Non-Example
• $2x + 3y = 0$: Matches $Ax+By=C$ → Example
• $x + y = 1$: Matches $Ax+By=C$ → Example
• $x = 6y$: Rearranges to $x - 6y = 0$, which fits $Ax+By=C$ → Example
• $y = x - 2$: Slope-intercept form → Non-Example

Answer:

Examples:

$5x - 3y = 9$
$2x + 3y = 0$
$x + y = 1$
$x = 6y$

Non-Examples:

$y = \frac{1}{6}x - 3$
$y = x - 2$