A rule is built from the plain rule y = x by first making it steeper and then shifting it up the page. Why must the steepening be done before the shift?

1. Working out an output from an input means multiplying by the rate first, then adding the starting value. 2. The picture has to match that arithmetic, so the steepening comes first and the shift second. 3. Taking the steps the other way round would add the shift before the multiplying, and the multiplying would then scale the shift as well. 4. That would give a different line, so the order is not free to choose. 5. Option A treats a shift as an undoing move, but shifting up and steepening are two separate changes. 6. Option B invents a rule about division that plays no part here, since the shift follows a multiplication. 7. Option D is wrong because steepening a slanted line never flattens it. _Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_