Let
[tex]A(-3,5)\ B(1,-1)[/tex]
we know that
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
Find the slope of the line AB
The slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Substitute the values
[tex]m=\frac{-1-5}{1+3}[/tex]
[tex]m=\frac{-6}{4}[/tex]
[tex]m=-\frac{3}{2}[/tex]
Find the equation of the line
Substitute the value of the slope and the point B
[tex]y-(-1)=-\frac{3}{2}(x-1)[/tex]
[tex]y+1=-\frac{3}{2}(x-1)[/tex]
therefore
the answer is the option
[tex]y+1=-\frac{3}{2}(x-1)[/tex]
