Review: Plan with Linear Rules
Evaluate linear models, recover them from tables, find inputs, and compare intersecting rules.
Bring the unit skills together
Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.
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Use the skills in a new task
Create a fictional print comparison memo. Booth A has table (1,$7), (3,$13), (5,$19) and follows a linear rule. Booth B uses y = 4x + 2. Derive A’s rule; find each booth’s cost for four posters; find the whole count that costs $19 at A; and find their equal-cost count. Explain the allowed inputs.
Work on paper or in your own document. Explain the choices you made.
- Derive A as y = 3x + 4 from a rate of $3/poster.
- Evaluate four posters as $16 at A and $18 at B.
- Solve 3x + 4 = 19 to get five posters.
- Solve 3x + 4 = 4x + 2 to get two posters and $10 at each.
- State that inputs are nonnegative whole poster counts.
Compare with a model response
A’s rate is (13 − 7)/(3 − 1) = 3, and its fixed fee is 7 − 3 = 4, so y = 3x + 4. Four posters cost $16 at A and $18 at B. At A, $19 means 3x = 15, or five posters. Equality gives x = 2 and $10 at both. Counts must be whole and nonnegative.
A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.