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Dividing x by y instead of y by x

In y = kx, k tells how much y there is for each one of x. Reversing the quotient changes the meaning.

Spot the wrong turn

For y = 7x, what is the constant of proportionality?

Incorrect answer: 1/7

Do not reverse y/x to x/y unless you also reverse the quantities in the equation. A straight line alone is insufficient: y = 3x + 2 is not proportional because it misses the origin.

Work it through

The correction

The coefficient of x in y = kx is k.

Decide which quantity is x and which is y, including their units.
For each nonzero x, calculate y ÷ x and check that the ratio stays constant.
Write y = kx and interpret k in the context. A nonzero starting fee means the relationship is not proportional.

Try the reasoning in another example

Three notebooks cost $7.50 at a constant price per notebook. Write cost C in terms of number n.

Divide total cost by number: 7.50 ÷ 3 = 2.50 dollars per notebook.
Multiply that unit price by n.

Answer: C = 2.50n

Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.

The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.

Your next step

Check this step for yourself

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