I understand how to prove on whether the function is a 1-to-1 or a onto function but i just can't figure out how did they get the equation in the beginning as the equation wasn't given in the question. Thank You!
2026-04-08 07:54:15.1775634855
Question on Cardinality
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$f$ is a restriction of a line which goes from through points $(x_1,y_1) = (2,-2)$ and $(x_2,y_2) = (5,3)$. Using the formula for the equation of a line through two points $$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$$ we obtain:
$$f(x) - (-2) = \frac{3 - (-2)}{5 - 2}(x - 2) \implies f(x) = \frac{5x-16}3$$