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, multiple each side of the equation by #color(red)(-2)# to give #y# a coefficient of #1# while keeping the equation balanced:
#color(red)(-2)(1/5x - 1/2y - 1) = color(red)(-2) xx 0#
#(color(red)(-2) xx 1/5x) - (color(red)(-2) xx 1/2y) - (color(red)(-2) xx 1) = 0#
#-2/5x + 2/2y + 2 = 0#
#-2/5x + 1y + 2 = 0#
#-2/5x + y + 2 = 0#
Now, add #color(red)(2/5x)# and subtract #color(blue)(2)# from each side of the equation to isolate #y# while keeping the equation balanced:
#-2/5x + y + 2 + color(red)(2/5x) - color(blue)(2) = 0 + color(red)(2/5x) - color(blue)(2)#
#-2/5x + color(red)(2/5x) + y + 2 - color(blue)(2) = 2/5x - 2#
#0 + y + 0 = 2/5x - 2#
#y = color(red)(2/5)x - color(blue)(2)#
