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Answer 1 · 2018-01-24T12:24:45

The equation of a straight line divides the plane into two halves

Let's first consider the equality:

#2x+5y=15#

This is the equation of a straight line, as follows:

#5y=-2x +15#, or in a more canonical form:

#y=-2/5x+3#

That is, the straight line with slope #-2/5# and #y# intercept #3#.

If you take #any# point #(x_1, y_1)# on that line, #y_1=-2/5x_1+3#

So #any# point #(x, y)# # below# that line satisfies #y<-2/5x+3#, or equivalently:

#2x+5y < 15#

That is, the solution is the half-plane #below# the straight line #y=-2/5x+3#