Step-by-step explanation:
Line is passing through the points
[tex] (-1,\:\: 3)=(x_1, \:\:y_1) \\\:\&\:\\
(-5, \:\:-3)=(x_2, \:\:y_2)[/tex]
Equation of line in two point form is given as:
[tex] \frac{y - y_1}{y_1 -y_2 } = \frac{x - x_1}{x_1 -x_2 } \\ \\ \therefore \: \frac{y - 3}{3 -( - 3)} = \frac{x - ( - 1)}{ - 1 -( - 5)} \\ \\ \therefore \: \frac{y - 3}{3 + 3)} = \frac{x + 1}{ - 1 + 5} \\ \\ \therefore \: \frac{y - 3}{6)} = \frac{x + 1}{ 4} \\ \\ \therefore \: 4(y - 3) = 6(x + 1) \\ \\ \therefore \: 4y - 12 = 6x + 6 \\ \\ \therefore \: 6x - 4y + 6 + 12 = 0 \\ \\ \therefore \: 6x - 4y + 18 = 0 \\ \\ \therefore \: 2(3x - 2y + 9) = 0 \\ \\ \purple { \boxed{\therefore 3x - 2y + 9= 0}} \\ is \: the \: required \: equation \: of \: line \\ [/tex]
