Find the equation of the line parallel to $\;$ $2x + 5y = 7$ $\;$ and making an intercept of $2$ on the $Y$ axis.
Equation of given line $\;$ $2x + 5y = 7$
i.e. $\;$ $y = \dfrac{-2}{5} x + \dfrac{7}{5}$
$\therefore \;$ Slope of the given line $= m = \dfrac{-2}{5}$
Since the required line is parallel to the given line,
slope of the required line $= m = \dfrac{-2}{5}$
$Y$ intercept of the required line $= c = 2$
$\therefore \;$ The equation of the required line is of the form: $\;$ $y = mx + c$
i.e. $\;$ $y = \dfrac{-2}{5}x + 2$
i.e. $\;$ $2x + 5y - 10 = 0$