The equation of the line passing through point $ \left(-\dfrac{ 2 }{ 3 },~2\right) $, and point $ \left(-3,~\dfrac{ 1 }{ 3 }\right) $ is:
$$ 15x-21y+52=0 $$To find equation of the line passing through points $ A(x_A,y_A) $ and $ B(x_B,y_B) $, we use formula:
$$ y - y_A~=~\frac{y_B - y_A}{x_B - x_A}(x-x_A) $$In this example we have:
$$ \begin{aligned} & \left(-\dfrac{ 2 }{ 3 },~2\right) \implies x_A = -\frac{ 2 }{ 3 } ~~\text{and}~~ y_A = 2 \\[1 em] & \left(-3,~\dfrac{ 1 }{ 3 }\right) \implies x_B = -3 ~~\text{and}~~ y_B = \frac{ 1 }{ 3 } \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 2~&=~\frac{ \frac{ 1 }{ 3 } - 2 }{ -3 - \left(-\frac{ 2 }{ 3 }\right) } \left( x - \left(-\frac{ 2 }{ 3 }\right) \right) \\[1 em]y - 2 ~&=~ \frac{ 5 }{ 7 } \left( x + \frac{ 2 }{ 3 } \right) \\[1 em]y - 2 ~&=~ \frac{ 5 }{ 7 }x + \frac{ 10 }{ 21 } \\[1 em]y ~&=~ \frac{ 5 }{ 7 }x + \frac{ 52 }{ 21 } \end{aligned} $$