Write as a Vector Equality x-4y=4 , y=1/4x-1

Problem

x−4*y=4,y=1/4*x−1

Solution

1. Identify that both equations represent the same line. Rearranging the first equation x−4*y=4 for y yields −4*y=−x+4 which simplifies to y=1/4*x−1

2. Parameterize the variables by letting x be a free parameter t

3. Express the variables x and y in terms of t

x=t

y=1/4*t−1

4. Write the system in vector form by separating the constant terms from the terms containing the parameter t

[[x],[y]]=[[0],[−1]]+[[t],[1/4*t]]

5. Factor out the parameter t to obtain the standard vector equation of a line.

[[x],[y]]=[[0],[−1]]+t*[[1],[1/4]]

Final Answer

[[x],[y]]=[[0],[−1]]+t*[[1],[1/4]]

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