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Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Use consistent coordinate differences to calculate slope.
- 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
Find the slope through (−2,5) and (4,−1).
Why this math matters
Name output units per input unit when interpreting a line's rate of change. 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.
Compute a signed rate from two points
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find the slope through (−2,5) and (4,−1).
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
Δy=−1−5=−6
The vertical output falls by six as we move to the second point.
Develop the calculation
Δx=4−(−2)=6
The horizontal input increases by six.
Check and interpret
m=Δy/Δx=−1
For each unit right, the line drops one unit.
The result
m=Δy/Δx=−1
For each unit right, the line drops one unit.
Common mistakes to catch
- Do not reverse only one coordinate difference.
- A zero horizontal difference makes the slope undefined.
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 is the slope through (1,2) and (5,10)?
Show a hint
Use the same point order in both differences.
Reveal answer and explanation
2
(10−2)/(5−1)=8/4=2.
Practice 2
What if you reverse the point order in both differences?
Show a hint
Both numerator and denominator change sign.
Reveal answer and explanation
The slope is unchanged
The two negative signs cancel in the quotient.
Take the idea with you
Name output units per input unit when interpreting a line's rate of change.
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: Build a line from a point and a rate
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