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:

$$ \begin{aligned} & \left(0,~\dfrac{ 1 }{ 2 }\right) \implies x_A = 0 ~~\text{and}~~ y_A = \frac{ 1 }{ 2 } \\[1 em] & \left(6,~0\right) \implies x_B = 6 ~~\text{and}~~ y_B = 0 \end{aligned} $$

After substituting into the formula, we obtain:

$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - \frac{ 1 }{ 2 }~&=~\frac{ 0 - \frac{ 1 }{ 2 } }{ 6 - 0 } \left( x - 0 \right) \\[1 em]y - \frac{ 1 }{ 2 } ~&=~ -\frac{ 1 }{ 12 } \left( x - 0 \right) \\[1 em]y - \frac{ 1 }{ 2 } ~&=~ -\frac{ 1 }{ 12 }x + 0 \\[1 em]y ~&=~ -\frac{ 1 }{ 12 }x + \frac{ 1 }{ 2 } \end{aligned} $$

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