Abstract: A new mathematical graph board for teaching linear equations and linear inequalities. The inventive device includes a board having an outer peripheral edge. The board includes a pair of peg boards secured within the outer peripheral edge. The pair of peg boards have a plurality of apertures therethrough. One of the peg boards has a four quadrant system disposed thereon. A plurality of graphing lines couple with the peg boards of the board. Each of the graphing lines is defined by a pair of pegs dimensioned for being received within the apertures of the peg boards. The pair of pegs have an elastic band extending therebetween. The elastic band varies a length of the graphing lines.