Question

*15 points* I need a proper explanation please.

Answer 1

To find our solution, we first write the equation in the following form:
$y = ax + b$

In this formula a represents the slope, therefore:
$y = - \frac{1}{5} x + b$

Because the line passes through the point P(5, -7), we can fill in the coordinates of this point in the formula and we get the following:
$- 7 = -\frac{1}{5} \times 5 + b$
$- 7 = -1 + b$
Now, add up 1 to both sides and we get
$b = -6$
So the formula will be:
$y = - \frac{1}{5} x - 6$

Bringing x to the other sides gives us:
$\frac{1}{5} x + y = -6$
Finally we multiply by 5 to get our standard form (and therefore our final answer):
$x + 5y = -30$
Hence, the answer is D.