When two lines are perpendicular, the product of their slopes are equal to -1.

The equation -2x + My = 5 written in slope-intercept form is

Y = \frac{2x}{M} +\frac{5}{M}

The slope of this is \frac{2}{M}

Similarly the equation 4y + x = -9 written in slope-intercept form is

y = \frac{-x}{4} -\frac{9}{4}

The slope of this is \frac{-1}{4}

The product of these slopes is equal to -1.

so,

\frac{2}{M}\ \times\frac{-1}{4}\ =-1

Solve for M to get,

M = \frac{1}{2}

I found an answer from math.stackexchange.com

high school **line equation** question - Mathematics Stack Exchange

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