Learn with Amar
Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Derive equations for horizontal and vertical lines.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Compare the lines through (2,4),(7,4) and through (3,−1),(3,6).
Why this math matters
Classify constant-output and constant-input relationships before choosing an equation form. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Distinguish zero slope from undefined slope
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Compare the lines through (2,4),(7,4) and through (3,−1),(3,6).
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
First pair: Δy=0, Δx=5
The output remains four while input changes.
Develop the calculation
Second pair: Δy=7, Δx=0
The input remains three while output changes.
Check and interpret
First line: y=4, slope 0; second: x=3, slope undefined
Division by zero is undefined; it does not produce zero or an ordinary infinite real slope.
The result
First line: y=4, slope 0; second: x=3, slope undefined
Division by zero is undefined; it does not produce zero or an ordinary infinite real slope.
Common mistakes to catch
- Zero slope requires zero rise and nonzero run.
- A vertical line cannot be written as y=mx+b with a finite real m.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
What equation describes a horizontal line through (−5,2)?
Show a hint
Its y-coordinate is constant.
Reveal answer and explanation
y=2
Every point has vertical coordinate two.
Practice 2
Does x=3 define y as a function of x?
Show a hint
One input three has many outputs.
Reveal answer and explanation
No
The vertical line fails the single-output condition.
Take the idea with you
Classify constant-output and constant-input relationships before choosing an equation form.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Use slope to compare nonvertical directions
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