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 + t 1y -3 + 2( )( ) ( )

x = 4 + 3t

y = 1 + 5t

t = (x – 4) / 3

t = (y - 1) / 5 x – 4 = y - 1

3 5

5x – 20 = 3y - 3

3y – 5x + 17 = 0

Finding the Cartesian Equation from a vector equation

X = 4 + t 3y 1 + 5( )( )( )

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 3y -9 + 5( )( )( )

So (-2, -9 ) is on the line

1

5/3( )

3

5( )or