The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
Therefore, first, add #color(red)(54x)# to each side of the equation to isolate the #y# term on the left side of the equation while keeping the equation balanced:
#9y - 54x + color(red)(54x) = color(red)(54x) + 18#
#9y - 0 = 54x + 18#
#9y = 54x + 18#
Now, divide each side of the equation by #color(red)(9)# to solve for #y# while keeping the equation balanced:
#(9y)/color(red)(9) = (54x + 18)/color(red)(9)#
#(color(red)(cancel(color(black)(9)))y)/cancel(color(red)(9)) = (54x)/color(red)(9) + 18/color(red)(9)#
#y = color(red)(6)x + color(blue)(2)#
