Answer:
[tex] y = -\frac{1}{3}x-2[/tex]
Step-by-step explanation:
From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]
(There are many other points in the table and any two of them can chosen as per our convenience)
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-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\
\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\
\therefore 6(y + 2) = - 2(x)\\
\therefore 6y + 12 = - 2x \\
\therefore 6y = - 2x - 12\\\\
\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\
\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]
