X = 2 + t y = -3 + 2t t = x – 2 t = (y + 3)/2 x – 2 = y + 3 2 2x – 4 = y + 3 y – 2x + 7 = 0 Finding the Cartesian Equation from a vector equation x = 2.

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x = 2 + t y = t t = x – 2 t = (y + 3)/2 x – 2 = y x – 4 = y + 3 y – 2x + 7 = 0 Finding the Cartesian Equation from a vector equation x = 2 + t 1 y ( )

x = 4 + 3t y = 1 + 5t t = (x – 4) / 3 t = (y - 1) / 5 x – 4 = y x – 20 = 3y - 3 3y – 5x + 17 = 0 Finding the Cartesian Equation from a vector equation X = 4 + t 3 y ( )

x = -2 y = -9 Gradient is 5/3 so vector in the line is 3y – 5x + 17 = 0 Finding the Vector Equation from a Cartesian equation X = -2 + t 3 y ( ) So (-2, -9 ) is on the line 1 5/3 ( ) 3 5 ( ) or