Answer :
y + 3 = -3/2(x - 2)
Explanationthe point-slope formula says
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where \\ m\text{ is the slope} \\ P1(x_1,y_1)\text{ is a well know point from the line} \end{gathered}[/tex]so
Step 1
find the slope of the line:
to find the slope we need to use the formula
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ and \\ P2(x_2,y_2) \\ are\text{ 2 points from the line} \end{gathered}[/tex]so
a)let
[tex]\begin{gathered} P1(2,-3)\text{ } \\ P2(-2,3) \end{gathered}[/tex]b) now replace in the formula
[tex]\begin{gathered} slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{3-(-3)}{-2-2}=\frac{6}{-4}=-\frac{3}{2} \end{gathered}[/tex]so, the slope is -3/2
Step 2
now, we can replace in the point-slope formula
a)let
[tex]\begin{gathered} P1(2,-3) \\ slope=m=-\frac{3}{2} \end{gathered}[/tex]b) now, replace
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-(-3)=-\frac{3}{2}(x-2) \\ y+3=-\frac{3}{2}(x-2) \end{gathered}[/tex]so, the answer is
y + 3 = -3/2(x - 2)
I hope this helps you