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:

$$ \begin{aligned} & \left(2,~3\right) \implies x_A = 2 ~~\text{and}~~ y_A = 3 \\[1 em] & \left(4,~7\right) \implies x_B = 4 ~~\text{and}~~ y_B = 7 \end{aligned} $$

After substituting into the formula, we obtain:

$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 3~&=~\frac{ 7 - 3 }{ 4 - 2 } \left( x - 2 \right) \\[1 em]y - 3 ~&=~ 2 \left( x - 2 \right) \\[1 em]y - 3 ~&=~ 2x-4 \\[1 em]y ~&=~ 2x-1 \end{aligned} $$

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