Answer:
[tex]y=-\frac{5}{9}x-\frac{2}{9}[/tex]
Step-by-step explanation:
[tex](-4,2)=(x_1,y_1)\\(5,-3)=(x_2,y_2)\\[/tex]
Substitute values into the given equation ;
[tex]\frac{y-y_1}{x-x_1}= \frac{y_2-y_1}{x_2-x_1} \\\\\frac{y - 2}{x - (-4)}= \frac{-3-2}{5-(-4)}\\ \\Simplify \\\frac{y-2}{x +4}= \frac{-3-2}{5+4} \\\\\frac{y-2}{x+4}= \frac{-5}{9} \\\\Cross\:Multiply\\9(y-2)=-5(x+4)\\\\Expand\\9y -18=-5x -20\\\\Collect\:like\:terms\\9y = -5x-20+18\\\\9y = -5x -2\\\\Divide \:through \:by \: 9\\\\\frac{9y}{9} = -\frac{5}{9} x -\frac{2}{9} \\\\y = -\frac{5}{9} x -\frac{2}{9} \\[/tex]
