First, multiply each side of the equation by #color(red)(12)# to put the equation in Standard Form for a linear equation. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
#color(red)(12)(x/3 + y/4) = color(red)(12) * 1#
#(color(red)(12) * x/3) + (color(red)(12) * y/4) = 12#
#color(red)(4)x + color(blue)(3)y = color(green)(12)#
The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#
Substituting for #color(red)(A)# and #color(blue)(B)# gives:
#m = -color(red)(4)/color(blue)(3)#
