-1/4
Explanation:Given equation:
[tex]4x\text{ - y = 9}[/tex]Rewriting the equation in the form y = mx + b:
[tex]\begin{gathered} 4x\text{ = y + 9} \\ 4x\text{ - 9 = y} \\ y\text{ = 4x - 9} \end{gathered}[/tex]For a line to be perpendicular to another line, the slope of one line will be the negative reciprocal of the second line.
From the equation above:
y = 4x - 9
m = slopeof the 1st line = 4
b = y - intercept = -9
reciprocal of the slope = 1/4
negative reciprocal = -1/4
slope of 2nd line = -1/4
The slope of the line perpendicular to the equation 4x - y = 9 is -1/4
