Write as a Vector Equality x=2t , y=4-t

Problem

x=2*t,y=4−t

Solution

1. Identify the components of the vector r by using the given parametric equations for x and y

2. Write the vector in component form by placing the expressions for x and y into a single vector.

r=<x,y>

3. Substitute the given expressions x=2*t and y=4−t into the vector.

r=<2*t,4−t>

4. Separate the vector into a constant vector and a vector containing the parameter t

r=<0,4>+<2*t,−t>

5. Factor out the parameter t from the second vector to express the equality in standard vector form.

r=<0,4>+t<2,−1>

Final Answer

<x,y>=<0,4>+t<2,−1>

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