# How do you find the parametric equations for a line segment?

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To find the parametric equations for a line segment between two points ( P_1(x_1, y_1) ) and ( P_2(x_2, y_2) ), you can use the following formulas:

[ x(t) = x_1 + (x_2 - x_1) \cdot t ] [ y(t) = y_1 + (y_2 - y_1) \cdot t ]

Where ( t ) varies from ( 0 ) to ( 1 ). These equations represent the ( x ) and ( y ) coordinates of points on the line segment as a function of the parameter ( t ). When ( t = 0 ), the equations yield the coordinates of ( P_1 ), and when ( t = 1 ), they yield the coordinates of ( P_2 ).

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