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Decide If a Relationship Is Proportional

Students examine tables, graphs, and equations to determine whether two quantities are in a proportional relationship. They check whether all ratios y/x are equal and whether the graph is a straight line passing through the origin.

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Decide If a Relationship Is Proportional

Grade 7 · Ratios and Proportional Relationships · question 1 of 3

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20 rungs. A star at the top.

Quick Cab charges $5 for 2 miles and $10 for 4 miles. Main Street Cab charges $14 for 4 miles and $28 for 8 miles. Which offer's cost is proportional to the number of miles?

How it is taught

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A proportional relationship has a constant y over x.

That constant is the multiplier from x to y.

Its graph is a straight line through the origin.

Read it: Is a table proportional?

Table B has x 3, 4, 6 and y 9, 12, 18: 9 ÷ 3 = 3, and 3 × 4 = 12, 3 × 6 = 18. One k, 3, takes every x to its y, so B is proportional: y = 3x.

  1. Find k from the first pair: y ÷ x.
  2. Multiply every other x by that k.
  3. If every y matches, the table is proportional. If one misses, it is not.

A proportional table has one k for every pair, so y = kx all the way along.

Table A adds 6 to each x: its y values are 9, 10, 12. A constant difference is not a constant ratio.

Table C misses at its last pair: 3 × 6 = 18, not 19.

Proportional means one k: every y ÷ x is the same number.

Calling table A proportional because each y is 6 more than its x.

Proportional means times, not plus: 3 × 4 = 12, not 10, so A has no one k.

The table with x 2, 3, 5 and y 14, 21, 35 is proportional. What is k? — 7. 14 ÷ 2 = 7, and 7 × 3 = 21, 7 × 5 = 35: one k, so y = 7x.

Hours vs Pay — is it proportional?

Maya walks dogs to earn money. We want to know — is her pay proportional to the hours she works?

Here's a table of her hours and her pay.

To check, we find y divided by x for every row. If they're all the same, the relationship is proportional.

Row one: five divided by one is five.

Row two: ten divided by two is also five.

Row three: fifteen divided by three is five again.

All three ratios equal five — that's a match!

We call that shared number the constant of proportionality, and we name it k. Here, k equals five.

So we can write the equation y equals five x.

Yes — Maya's pay is proportional to her hours. She earns five dollars per hour.

Is pay proportional to hours?Maya walks dogs · paid by the hourHours (x)Pay ($)15210315y ÷ x5 ÷ 1 = 510 ÷ 2 = 515 ÷ 3 = 5All ratios = 5 ✓k = 5 (constant of proportionality)y = 5xPROPORTIONAL?Yesk = 5 ($/hr)
Grade 7 · Test using the ratio y ÷ x

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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