The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The equation of the given line is
3x + 5y = 7
5y = 7 - 3x
5y = - 3x + 7
y = - 3x/5 + 7/5
By comparing with the equation of the given line, slope of the given line is - 3/5
If two lines are parallel, it means that they have the same slope. This means that the slope of the line passing through (5, - 6) is - 3/5
We would determine the y intercept, c by substituting m = - 3/5, x = 5 and y = - 6 into the slope intercept equation. It becomes
- 6 = - 3/5 * 5 + c
- 6 = - 3 + c
c = - 6 + 3
c = - 3
By substituting m = - 3/5 and c = - 3, into the slope intercept equation, the equation of the line would be
y = - 3x/5 - 3