Kenneth ChengMathematical modeling
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A line has inclination 135°. Find its slope.

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 / Foundation#Your turn

A line has inclination 135°. Find its slope.

m=tan⁡135∘m=\tan135^\circ
  • A vertical line has no finite slope; m1m2=−1 applies only when both slopes exist.
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.
tan⁡(180∘−45∘)=−tan⁡45∘\tan(180^\circ-45^\circ)=-\tan45^\circ
Worked solution

  1. Translate the geometric condition into a coordinate equation.

  2. Apply the stated relation and retain its conditions.

    m=−1m=-1

  3. Inclination lies in [0°,180°); a second-quadrant angle has negative tangent.

The requested value is -1.

Checks and common pitfalls: Inclination lies in [0°,180°); a second-quadrant angle has negative tangent.

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 ↗