6x+4y=72
First, we will find the slope of the line above
Rearranging the above equation in the form y =mx + b
where m is the slope
6x+4y=72
subtract 6x from both-side of the equation
4y = -6x + 72
divide through the equation by 4
y = -6x/4 + 72/4
y =-3/2 x + 18
comparing the above with y=mx + b
m₁ = -3/2
To find the slope of a line that is perpendicular to the equation;
Let the slope of that line be m₂
For perpendicular equations;
m₁ m₂ = -1
substitute for m₁ and solve for m₂
That is;
-3/2 m₂ = -1
multiply both-side of the equation by -2/3
m₂ = 2/3
Hence the slope of line perpendicular to the line whose equation is 6x+4y=72 is 2/3