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Here are the steps to solve this problem:

Find the gradient (slope) of the given line.
The equation of the given line is $y - 4x + 3 = 0$ .
Rearrange this equation into the slope-intercept form $y = mx + c$ :
$y = 4x - 3$
The gradient of this line is $m_1 = 4$ .
Find the gradient of the perpendicular line.
A perpendicular line has a gradient that is the negative reciprocal of the original line's gradient.
$m_2 = -\frac{1}{m_1} = -\frac{1}{4}$
Use the gradient of the perpendicular line and the point $(-8, 5)$ to find the equation of the line.
We use the point-slope formula: $y - y_1 = m(x - x_1)$ .
Here $m = -\frac{1}{4}$ , $x_1 = -8$ , and $y_1 = 5$ .
$y - 5 = -\frac{1}{4}(x - (-8))$ $y - 5 = -\frac{1}{4}(x + 8)$
To eliminate the fraction, multiply both sides by 4:
$4(y - 5) = -1(x + 8)$ $4y - 20 = -x - 8$
Rearrange the equation into the standard form ( $Ax + By + C = 0$ ).
$x + 4y - 20 + 8 = 0$ $x + 4y - 12 = 0$

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