Find the equation of the line that is parallel to 2x + 5y - 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and (-4, 1).

Given equation of line,

⇒ 2x + 5y - 7 = 0

Converting it in the form y = mx + c,

⇒ 5y = -2x + 7

⇒ y = $-\dfrac{2}{5}x + \dfrac{7}{5}$

So, the slope is $-\dfrac{2}{5}$.

Since, slope of parallel lines are equal. So, slope of parallel line will be $-\dfrac{2}{5}$

By mid-point formula, the mid-point of the line segment joining the points (2, 7) and (-4, 1) is

$\Big(\dfrac{2 + (-4)}{2}, \dfrac{7 + 1}{2}\Big)$ = (-1, 4).

Equation of the line having slope = $-\dfrac{2}{5}$ and passing through (-1, 4) can be given by,

$\Rightarrow y - y$1 = m(x - x1) \\[1em] \Rightarrow y - 4 = -\dfrac{2}{5}(x - (-1)) \\[1em] \Rightarrow 5(y - 4) = -2(x + 1) \\[1em] \Rightarrow 5y - 20 = -2x - 2 \\[1em] \Rightarrow 5y + 2x = 20 - 2 \\[1em] \Rightarrow 2x + 5y = 18 \\[1em] \Rightarrow 2x + 5y - 18 = 0.

Hence, the equation of the line is 2x + 5y - 18 = 0.