Find the equation of the line passing through $\left(2, 3\right)$ and parallel to the line $5x + 4y = 6$
Equation of given line $\;$ $5x + 4y = 6$
i.e. $\;$ $y = \dfrac{-5}{4} x + \dfrac{6}{4}$
$\therefore \;$ Slope of the given line $= m = \dfrac{-5}{4}$
Since the required line is parallel to the given line,
slope of the required line $= m = \dfrac{-5}{4}$
The required line passes through the point $\left(x_1, y_1\right) = \left(2, 3\right)$
$\therefore \;$ The equation of the required line is of the form: $\;$ $y - y_1 = m \left(x - x_1\right)$
i.e. $\;$ $y - 3 = \dfrac{-5}{4} \left(x - 2\right)$
i.e. $\;$ $4y - 12 = -5x + 10$
i.e. $\;$ $5x + 4y - 22 = 0$