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The equation of a line passing through $(5, 6)$ and $(4, 2)$ is

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$4 x + y - 14 = 0$

$4 x - y + 14 = 0$

$4 x - y - 14 = 0$

$4 x + y + 14 = 0$

answer is C.

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Detailed Solution

Two-points from of a line

$\begin{array}{l} y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1}) \\ y - 6 = \frac{2 - 6}{4 - 5} (x - 5) \\ y - 6 = \frac{- 4}{- 1} (x - 5) \\ y - 6 = 4 x - 20 \\ 4 x - y - 14 = 0 \end{array}$

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