2. Let $l$ be a line in the Cartesian plane given by $l = \{(x, y) | y = mx + b\}$. Let distance be measured by the square metric. That is, for $A = (x_1, y_1)$, $B = (x_2, y_2)$, let $AB = \max\{|x_2 - x_1|, |y_2 - y_1|\}$. Find a bijective function $f : l \to \mathbb{R}$ such that $|f(B) - f(A)| = AB$.
3. Consider the function $f$ from the previous exercise.
(a) Prove that $f$ is injective.
(b) Prove that $f$ is surjective.
(c) Prove that $|f(B) - f(A)| = AB$ where $AB$ is given by the square metric.