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:

$$ \begin{aligned} & \left(50,~255\right) \implies x_A = 50 ~~\text{and}~~ y_A = 255 \\[1 em] & \left(500,~0\right) \implies x_B = 500 ~~\text{and}~~ y_B = 0 \end{aligned} $$

After substituting into the formula, we obtain:

$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 255~&=~\frac{ 0 - 255 }{ 500 - 50 } \left( x - 50 \right) \\[1 em]y - 255 ~&=~ -\frac{ 17 }{ 30 } \left( x - 50 \right) \\[1 em]y - 255 ~&=~ -\frac{ 17 }{ 30 }x + \frac{ 85 }{ 3 } \\[1 em]y ~&=~ -\frac{ 17 }{ 30 }x + \frac{ 850 }{ 3 } \end{aligned} $$

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