#x#-intercept means the point where the lines reaches the #x#-axis which means #y=0#
#y#-intercept means the point where the lines reaches the #y#-axis which means #x=0#
To find #y#-intercept, there is also another method which is by using the formulae itself, which is #y=mx+c# where #c# stands for #y#-intercept.
Regarding your question, to find #y#-intercept using
[#y=mx+c# method]
#=> 7x + 8y = 18#
#=> y = (18-7x)/8#
#=> y = (18)/8 - (7x)/8#
#=> y = -(7x)/8 + (18)/8#
#:. y#-intercept = #18/8#
Or apply #x=0#
#=> 8y = 18#
#:. y# -intercept = #18/8#
To find #x#-intercept, apply #y=0#
#=> 18/8 = (7x)/8#
#=> 144 = 56x#
#:. x#-intercept = #18/7#