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.
First, subtract #color(red)(14x)# from each side of the equation to isolate the #y# term:
#-color(red)(14x) + 14x - 19y = -color(red)(14x) + 1#
#0 - 19y = -14x + 1#
#-19y = -14x + 1#
Now, divide both sides of the equation by #color(red)(-19)# to put the equation in slope-intercept form while keeping the equation balanced:
#(-19y)/color(red)(-19) = (-14x + 1)/color(red)(-19)#
#(color(red)(cancel(color(black)(-19)))y)/cancel(color(red)(-19)) = (-14x)/color(red)(-19) + 1/color(red)(-19)#
#y = (-14)/(-19)x - 1/19#
#y = color(red)(14/19)x - color(blue)(1/19)#
