Answer:
3x +8y = -17
Explanation:
The point-slope equation is a good place to start.
y -k = m(x -h) . . . . . equation through (h, k) with slope m
Filling in your numbers gives ...
y +4 = -3/8(x -5)
Multiplying by 8, we get
8y + 32 = -3x + 15
Adding 3x-32 puts this in standard form.
3x + 8y = -17
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Standard form is ...
ax +by = c
where a, b, c are mutually-prime integers and the leading coefficient is positive. (If a=0, the leading coefficient is b.)