Question

the equation ( 14x - 2y = -18 ) is in standard form. which process proves that it is a linear function?
create a table like this one.

x	y
1	16
2	23

as the x - values increase by one, the y - values double. the pattern will continue. it is a linear function.
look for common factors in the coefficients and constants. since 14, -2, and -18 are all divisible by negative two, we can write the equation like this:
( 7x + y = 9 )
since the numbers 7, 1, and 9 are integers, it is a linear function.
write the equation in a different form, where ( y = ) is the first part, like this:
( y = -7x + 9 )
there are two terms after the equals sign, which means it is a linear function.
create a table like this one.

x	y
1	16
2	23

Explanation:

A linear function can be written in the slope-intercept form $y=mx+b$, where $m$ and $b$ are constants. Converting the given standard form equation to this explicit slope-intercept form confirms it fits the linear function definition. The other options have errors: the first table's reasoning about y-values doubling is wrong (they increase by 7), simplifying to integer coefficients alone does not prove linearity, and the last table's reasoning is incomplete without verifying a constant rate of change.

Answer:

Write the equation in a different form, where $y =$ is the first part, like this:
$y = -7x + 9$
There are two terms after the equals sign, which means it is a linear function.