Kenneth ChengMathematical modeling
← Senior Mathematics Studio

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Find C so that Ax+By+C=0 passes through P.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Equations of lines and circles: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

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

01 / Standard#Your turn

Find C so that Ax+By+C=0 passes through P.

A=2, B=−3, P=(26,1)A=2,\ B=-3,\ P=(26,1)
  • Point-slope form omits vertical lines; intercept form requires nonzero intercepts.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Translate the geometric condition into a coordinate equation.
Hint 2
Use this intermediate relation.
C=−AxP−ByPC=-Ax_P-By_P
Worked solution

  1. Translate the geometric condition into a coordinate equation.

  2. Apply the stated relation and retain its conditions.

    C=−2(26)+3=−49C=-2(26)+3=-49

  3. A point satisfies the equation exactly when the substituted expression is zero.

The requested value is -49.

Checks and common pitfalls: A point satisfies the equation exactly when the substituted expression is zero.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗