[tex]\btext{x+5y=-10}[/tex]
Step-by-step explanation:
When two lines are parallel,their slopes are equal.
Given line is [tex]x+5y=45[/tex].
Let [tex]m[/tex] be the slope of the line.
[tex]m=-5[/tex].
It is given that the line passes through the point [tex](5,-3)[/tex].
The equation of the line passing through [tex](x_{1},y_{1})[/tex] and has slope [tex]m[/tex] is [tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]x_{1}=5[/tex]
[tex]y_{1}=-3[/tex]
[tex]m=-5[/tex]
So, the equation is [tex]y-5=-5(x+3)[/tex]
which simplifies to [tex]x+5y=-10[/tex]
