Describe a Supplied Paired Record
A scatter representation plots each input with its paired output.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: A supplied scatter record has pairs (1,2), (2,4), (3,6), (4,8). Which description fits? Candidate answers: (A) Negative linear association (B) No change in y as x changes (C) Positive linear association in this record (D) The record proves x causes y.
- Independent check inputs: A supplied scatter record has pairs (1,3), (2,5), (3,7), (4,9). Which description fits? Candidate answers: (A) Negative linear association (B) No change in y as x changes (C) Positive linear association in this record (D) The record proves x causes y.
Learn the idea
Paired measurements describe how two variables vary together. A trend line summarizes association, predicted outputs can be compared with observations using residuals, and the observed input range limits how confidently that trend can be extended. A scatter representation plots each input with its paired output. A rising pattern indicates positive association in the supplied record, whereas a straight pattern adds a claim about linear structure.
Here is the method on the supplied teaching case. Each increase of 1 in x accompanies an increase of 2 in y; the four points lie on a rising line. Association in the record does not identify a cause.
Association does not establish causation. The supplied exact pattern is small and artificial; describe its direction and form without generalizing to unobserved people, future measurements or a causal mechanism.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: A supplied scatter record has pairs (1,2), (2,4), (3,6), (4,8). Which description fits? Candidate answers: (A) Negative linear association (B) No change in y as x changes (C) Positive linear association in this record (D) The record proves x causes y. Solution: Each increase of 1 in x accompanies an increase of 2 in y; the four points lie on a rising line. Association in the record does not identify a cause. The final answer is Positive linear association in this record. Association does not establish causation. The supplied exact pattern is small and artificial; describe its direction and form without generalizing to unobserved people, future measurements or a causal mechanism.
Check your reasoning
Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.
Helpful tips
- A scatter representation plots each input with its paired output.
- Association does not establish causation.
See the answer and explanation
Positive linear association in this record
Each increase of 1 in x accompanies an increase of 2 in y; the four points lie on a rising line. Association in the record does not identify a cause.
Take it further
Changed-input task: A supplied scatter record has pairs (1,9), (2,11), (3,13), (4,15). Which description fits? Candidate answers: (A) Negative linear association (B) No change in y as x changes (C) Positive linear association in this record (D) The record proves x causes y. Show the mathematical reason, not only the selected answer. Expected result: Positive linear association in this record. Each increase of 1 in x accompanies an increase of 2 in y; the four points lie on a rising line. Association in the record does not identify a cause.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
Your choices are temporary. Feedback appears after you check all the answers.
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Check the subject sources
- California Department of Education: adopted mathematics standards
- OpenStax: Functions and function notation
These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.