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What the numbers in a rule mean worksheets

y = −20x + 300 gives the litres in a tank after x minutes. How much was in it at the start, and how much drains each minute? These free printable worksheets hand over the rule and the situation and ask what the two numbers say.

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What the numbers in a rule mean
What the numbers in a rule mean worksheet — Start and rate, rising and falling, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

This is the companion sheet to writing a rule from a story, and it runs the other way: a student can assemble y = 12x + 25 from a sentence and still not be able to say what the 12 is when handed the rule alone. The numbers appear ONLY in the equation — the situation is a phrase with no figures in it — so the question cannot be answered by matching a number in the prose to a number in the rule.

Why this sheet works

The two facts behind every answer are worth saying once: putting x = 0 leaves the constant behind, so that number is where the story starts; and going from x to x + 1 adds the coefficient, so that number is what one step does. The worked walk substitutes rather than asserts, because that is a check a student can run on any rule they ever meet.

How this one works

What does the rule start at?

x=0
y = −2 × 0 + 45=45
45
  1. The start of the story is x = 0 — before any days have passed.
  2. Put 0 in for x: −2 × 0 is 0, so the whole first term disappears and only 45 is left.
  3. So the number added on the end is always where the story begins. Here that is 45.

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