Answer:
The second option is correct. The point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex].
Step-by-step explanation:
The given points are A(-3,5) and B(1,-1).
Slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of AB is
[tex]m=\frac{-1-5}{1-(-3)}[/tex]
[tex]m=\frac{-6}{4}[/tex]
[tex]m=\frac{-3}{2}[/tex]
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope of the line.
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (-3,5). The point slope form of AB is
[tex]y-5=\frac{-3}{2}(x+3)[/tex]
Case 1: The slope of the line is [tex]\frac{-3}{2}[/tex] and the point is (1,-1). The point slope form of AB is
[tex]y+1=\frac{-3}{2}(x-1)[/tex]
Therefore the point slope form of AB is [tex]y+1=\frac{-3}{2}(x-1)[/tex]. Option 2 is correct.
