Answer:
[tex]3x+5y=-5[/tex]
Step-by-step explanation:
First, we can put the given information into an equation in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex] when [tex](x_1,y_1)[/tex] is the given point and [tex]m[/tex] is the slope
Plug in the point (-5,2)
[tex]y-2=m(x-(-5))\\y-2=m(x+5)[/tex]
Plug in the slope [tex]\frac{-3}{5}[/tex]
[tex]y-2=\frac{-3}{5} (x+5)[/tex]
Open up the parentheses
[tex]y-2=\frac{-3}{5} (x+5)\\y-2=\frac{-3}{5}x+\frac{-15}{5} \\y-2=\frac{-3}{5}x-3[/tex]
Multiply all values by 5 to rid the fraction
[tex]5y-10=-3x-15[/tex]
Add 3x to both sides
[tex]3x+5y-10=-3x-15+3x\\3x+5y-10=-15[/tex]
Add 10 to both sides
[tex]3x+5y-10+10=-15+10\\3x+5y=-5[/tex]
I hope this helps!
