Kenneth ChengMathematical modeling
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If x increases by 4, how does y change?

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TOPIC 01

2024 JM01

The minus sign outside the product changes both inner signs.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

If x increases by 4, how does y change?

4x+5y=x(y+1)−(x−1)(y−1)4x+5y=x(y+1)-(x-1)(y-1)

Official paper · jm01-2024 · I.3 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Decreases by 8
  2. Decreases by 4
  3. Decreases by 2
  4. Increases by 4
  5. Increases by 8

Working and explanation

BUILD THE REASONING

Hint 1
Expand the right-hand side carefully.
Hint 2
Find the slope of y as a function of x.
Worked solution

  1. Cancel the xy terms.

    4x+5y=2x+y−1  ⟹  y=−x2−144x+5y=2x+y-1\implies y=-\frac x2-\frac14

  2. Multiply the slope by the change in x.

    Δy=−12(4)=−2\Delta y=-\frac12(4)=-2

C: y decreases by 2.

Checks and common pitfalls: The minus sign outside the product changes both inner signs.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Cancel the xy terms.
    4x+5y=2x+y−1  ⟹  y=−x2−144x+5y=2x+y-1\implies y=-\frac x2-\frac14
  • Multiply the slope by the change in x.
    Δy=−12(4)=−2\Delta y=-\frac12(4)=-2

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Curriculum and source notes ↗