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Lesson · Grade 7 · Mathematics

Reading the rule from a graph

  • Grade 7
  • Mathematics
  • 1 min 17 s
  • British Columbia
  • BC7-MA-38

Students read the points (1, 6), (2, 10), (3, 14) and (4, 18) off a graph and see that each step across 1 goes up 4, so the rule multiplies n by 4. Testing the first point shows it is 2 higher than 4n, which gives the rule Term = 4n + 2, and the point for n = 3 confirms it.

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In one sentence

The question this lesson answers

This graph shows a pattern, with the term number n across the bottom and the term up the side.

How can we find the rule that turns each n into its term?

Transcript

What the lesson says

This graph shows a pattern, with the term number n across the bottom and the term up the side.

How can we find the rule that turns each n into its term?

First, read each point: down to find n, and across to find the term.

The first point is at n equals 1, with a term of 6.

The other points have terms 10, 14 and 18.

From each point to the next, we go across 1 and up 4.

Going up 4 for each step across means the rule multiplies n by 4.

Test it on the first point. When n is 1, 4 times 1 is 4.

But the point is at 6, which is 2 more, so we add 2.

So the rule is 4 times n, plus 2.

Check the rule with another point, where n is 3.

4 times 3 is 12, plus 2 is 14, just like the graph.

To read the rule from a graph, multiply n by how far each step goes up, then use one point to find what to add or subtract.

Curriculum

Where this fits

British Columbia, Grade 7

Mathematics, Patterns and algebra: discrete linear relations, using expressions, tables, and graphsBC7-MA-38

Previous: Graphing a Linear Relation from Its TableNext: What the two numbers in 3n + 2 mean

The outcomes and strands follow the British Columbia curriculum.

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