A(3,4) is a point on a line having slope 2/3.write down the coordinates of nearby points on either side of this line having x and y coordinates as natural numbers

Dear student,
the point-slope form of a line is given as y-y1=m×(x-x1)y-4=23(x-3)3y-12=2x-63y=2x+6y=2x+63putting x=6 we get y=2×6+63=6 hence the coordinates are (6,6)similarly other coordinates can be found out using the above methodNote- x must be multiple of 3 in order to get Y as a natural number as the denominator is 3y-y1=m×(x-x1)y-4=23(x-3)3y-12=2x-63y=2x+6y=2x+63putting x=6 we get y=2×6+63=6 hence the coordinates are (6,6)similarly other coordinates can be found out using the above methodNote- x must be multiple of 3 in order to get Y as a natural number as the denominator is 3

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