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Equation of a line that passes through two points can find solve system of linear equations. Example. We can also use formula: Equation of a line that passes through points A = (x_1, y_1) and B = (x_2,y_2): (x_2-x_1)(y-y_1) = (y_2-y_1)(x-x_1). Example: The stright line that passes through points A = (2,5) and B = (3,7) has the equation: (3-2)(y-5) = (7-5)(x-2); 1(y-5) = 2(x-2); y-5 = 2x-4; y = 2x-4+5; y = 2x+1.