To find our solution, we first write the equation in the following form:
[tex]y = ax + b[/tex]
In this formula a represents the slope, therefore:
[tex]y = - \frac{1}{5} x + b[/tex]
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:
[tex] - 7 = -\frac{1}{5} \times 5 + b[/tex]
[tex] - 7 = -1 + b[/tex]
Now, add up 1 to both sides and we get
[tex]b = -6[/tex]
So the formula will be:
[tex]y = - \frac{1}{5} x - 6[/tex]
Bringing x to the other sides gives us:
[tex] \frac{1}{5} x + y = -6[/tex]
Finally we multiply by 5 to get our standard form (and therefore our final answer):
[tex]x + 5y = -30[/tex]
Hence, the answer is D.
