The line passing through (0, 2) and (-3, -1) is parallel to the line passing through (-1, 5) and (4, a). Find a.

By formula,

Slope = $\dfrac{y$2 - y1}{x2 - x1}

Let m₁ be the slope of line passing through (0, 2) and (-3, -1), and m₂ be the slope of line passing through (-1, 5) and (4, a).

Since, lines are parallel.

∴ m₁ = m₂

$\Rightarrow \dfrac{-1 - 2}{-3 - 0} = \dfrac{a - 5}{4 - (-1)} \\[1em] \Rightarrow \dfrac{-3}{-3} = \dfrac{a - 5}{5} \\[1em] \Rightarrow 1 = \dfrac{a - 5}{5} \\[1em] \Rightarrow a - 5 = 5 \\[1em] \Rightarrow a = 10.$

Hence, a = 10.