One rule links x and y

Mathematics · Ratio & Proportion · ages 14-15

Name ______________________ Date ____________

Which equation shows that y is directly proportional to x?
- y = kx
- y = x + k
- y = k/x
Which equation shows that y is directly proportional to x?
- y = kx
- y = x + k
- y = k/x
- y = x^2 + k
y is directly proportional to x. When x = 6, y = 18. Find k.
Answer: ______________
y is directly proportional to x. When x is 4, y is 20. What is k?
- 4
- 5
- 16
The pair (5, 40) fits a direct proportion, with x equal to 5 giving y equal to 40. What is k?
Answer: ______________
If y = kx and k = 8, then when x = 1, y must equal 8.
Circle one: True False
A pair of values in a direct proportion is (5, 40), meaning x = 5 gives y = 40. Find k.
Answer: ______________
y is directly proportional to x with k = 6. If y = 54, what is x?
- 6
- 7
- 8
- 9
y is directly proportional to x with k equal to 8. What is y when x is 12?
Answer: ______________
The pairs (1, 8) and (12, 96) both fit y equals k times x with the same k. Using that k, what is y when x is 15?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

y = kx · Only y equals k times x keeps the steady rate with no adding.
y = kx · Direct proportion means y is always x times the same constant k, with no adding or dividing by x.
3 · k is just y divided by x for any matching pair.
5 · Divide y by x: 20 divided by 4 is 5.
8 · Any single matching pair pins down k: 40 divided by 5 is 8.
True · Plugging x = 1 into y = kx always gives y = k.
8 · Any single matching pair is enough to pin down k.
9 · Going backwards from y to x means dividing by k instead of multiplying.
96 · Multiply k by the new x: 8 times 12 is 96.
120 · Both pairs give k equal to 8, and 8 times 15 is 120.