The question: PART 1: The graph of $x_2 = 4x_1 - 5$ is a line in $\mathbb{R}^2$. Give a precise interpretation of what the graph of the line represents with regards to solutions to the equation (do not use the words “slope,” “intercept,” or “vector” in your explanation).
PART 2: Write the solution set of this equation in the form $x = p + tv$. Use only that result to lists three specific solutions to the above equation. Show all your work.
For part 1, I'm not exactly sure what the question is asking for. At first I thought, wouldn't it just be "The solution set to a particular system can be represented by a line in $\mathbb{R}^3$ passing through the point $(-5, 0)$ and in the direction of the vector $(4,0)$. But then that uses the word "vector". And I'm not sure it answers exactly what the questions asks for.
Part two would just be $x_2 = (-5,0)+t(4)$
Not sure if this is the interpretation that is sought, but it is nonetheless valid: if $A = [-4 ~1]$ and $b=[5]$, then points on the line correspond to solutions of the matrix equation $Ax=b$, in which $$ x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}. $$
Technically, I didn’t use the word ‘vector’ although I clearly wrote $x$ as a vector — not sure if this disqualifies it.