Which of the following lines is parallel to $4x-3y=7$?

The correct option is $4x-3y=5$.

To determine which line is parallel to the given line, let us first find the slope of the given line equation:

$4x-3y=7$

We can convert this equation into slope-intercept form, which is $y=mx+c$, where $m$ is the slope.

Rearranging the terms:

$3y=4x-7$

$y=\frac{4}{3}x-\frac{7}{3}$

Thus, the slope of the given line is:

$m=\frac{4}{3}$

Parallel lines must have the exact same slope. Therefore, any line parallel to $4x-3y=7$ must also have a slope of $\frac{4}{3}$.

Lines of the general form $Ax+By=C$ have a slope equal to $-\frac{A}{B}$. For a line to be parallel, the ratio of the coefficients of $x$ and $y$ must remain equal to $4x-3y$.

Now, let us examine the given option:

$4x-3y=5$

Converting this line to slope-intercept form:

$3y=4x-5$

$y=\frac{4}{3}x-\frac{5}{3}$

The slope of this line is also $m=\frac{4}{3}$.

Since both lines have the same slope ($m=\frac{4}{3}$) but different y-intercepts, the line $4x-3y=5$ is parallel to $4x-3y=7$.