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Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to recover a linear rule from a table.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Slope, substitution, and two-step equations.
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
A model table lists (x,y) = (2,9), (4,15), (6,21). Assuming a linear rule, find y in terms of x and predict y when x = 10.
Why this math matters
A constant output change per input unit gives a linear rate, while substitution recovers the intercept. Identify the input step size before interpreting a numerical pattern as a rate.
Set up the model
A useful answer starts with clear assumptions:
- The relationship is linear over the input range in question.
- The table values are exact.
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.
Recover a linear rule from a table
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A model table lists (x,y) = (2,9), (4,15), (6,21). Assuming a linear rule, find y in terms of x and predict y when x = 10.
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 quantities
m = (15 − 9)/(4 − 2) = 6/2 = 3
The input increases by two each row, so divide the output change by two.
Apply the relationship
y = 3x + b; 9 = 3(2) + b; b = 3
Use a known row to recover the output at zero input.
Check and interpret
y = 3x + 3; y(10) = 33
The third listed row also checks: 3(6) + 3 = 21.
The result
y = 3x + 3; y(10) = 33
The third listed row also checks: 3(6) + 3 = 21.
Common mistakes to catch
- A row-to-row output change is not the slope unless the input change is one.
- A few points permit a linear model assumption but do not establish every real-world extrapolation.
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
A linear table contains (1,6) and (3,14). Find its rule.
Show a hint
Calculate slope first, then substitute one point.
Reveal answer and explanation
y = 4x + 2
The slope is 8/2 = 4; 6 = 4(1) + b gives b = 2.
Practice 2
For y = −2x + 7, what change in y occurs when x increases by 4?
Show a hint
Multiply the slope by the input change.
Reveal answer and explanation
y decreases by 8
Δy = −2(4) = −8; the intercept does not affect changes.
Take the idea with you
Identify the input step size before interpreting a numerical pattern as a rate.
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: Solve an equation that needs distribution
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