Kenneth ChengMathematical modeling
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A line through (1,2) is perpendicular to 2x−3y=4. Find its y-intercept.

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TOPIC 01

2022 JM01

A y-intercept has x=0.

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

01 / Standard#Your turn

A line through (1,2) is perpendicular to 2x−3y=4. Find its y-intercept.

Official paper · jm01-2022 · I.10 · PDF 3

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

Skills and prerequisite lessons
  1. Option A(0,7/2)(0,7/2)
  2. Option B(0,5/2)(0,5/2)
  3. Option C(0,3)(0,3)
  4. Option D(0,−1/2)(0,-1/2)
  5. Option E(0,3/2)(0,3/2)

Working and explanation

BUILD THE REASONING

Hint 1
The given line has slope 2/3.
Hint 2
Use perpendicular slope −3/2.
Worked solution

  1. Form the line equation.

    y−2=−32(x−1)y-2=-\frac32(x-1)

  2. Set x=0.

    y=2+3/2=7/2y=2+3/2=7/2

A: (0,7/2).

Checks and common pitfalls: A y-intercept has x=0.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Form the line equation.
    y−2=−32(x−1)y-2=-\frac32(x-1)
  • Set x=0.
    y=2+3/2=7/2y=2+3/2=7/2

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Curriculum and source notes ↗