Let's solve the problem step by step:

We need to find the equation of a line parallel to
$-6y = 48 - 6x$
and passing through the point $(7, 8)$.

Step 1: Find the slope of the given line

The equation is given as:
$-6y = 48 - 6x.$

1. Divide through by $-6$ to simplify:
   $y = -x + 8.$
2. This is now in slope-intercept form $y = mx + c$, where $m$ is the slope.
   Here, $m = -1$.

Step 2: Write the equation of the parallel line

Lines that are parallel have the same slope. So, the slope of the new line is also $m = -1$.

Using the point-slope form of a line equation:
$y - y_1 = m(x - x_1),$ where $(x_1, y_1) = (7, 8)$ and $m = -1$.

Substitute the values:
$y - 8 = -1(x - 7).$

Simplify the equation:
$y - 8 = -x + 7.$

Step 3: Check the options

Rearrange $y - 8 = -x + 7$:
$y - 8 = -(x - 7).$

This matches the second option:
$y - 8 = -(x - 7).$

Final Answer:

The correct option is:
$\boxed{y - 8 = -(x - 7)}.$

Do you need further clarification or more details? Let me know!

Related Questions:

1. How do you find the slope of a line given in standard form?
2. What is the point-slope form of a line, and how is it derived?
3. How do you determine if two lines are parallel?
4. How do you convert a line equation from slope-intercept form to standard form?
5. How would you write the equation of a line perpendicular to the given line through the same point?

Tip:

Always convert equations to slope-intercept form ($y = mx + b$) to easily identify the slope ($m$).