Answer:
A. [tex] y= - \frac{1}{3} x[/tex]
Step-by-step explanation:
Line is passing through the point [tex] (3,\:-1)=(x_1, \:y_1) [/tex] and origin [tex] (0,\: 0)=(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-(-1)}{-1-0}= \frac{x-3}{3-0}\\\\
\therefore \frac{y+1}{-1}= \frac{x-3}{3} \\\\
\therefore 3(y+1) = - 1(x-3)\\\\
\therefore 3y + 3 = - x +3\\\\
\therefore 3y = - x +3-3\\\\
\therefore 3y = - x\\\\
\huge \orange {\boxed {\therefore y= - \frac{1}{3} x}} [/tex]
