Grade 9 · Math · Algebra 1

9th grade Direct variation y = kx and inverse variation xy = k worksheet

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Direct variation y = kx and inverse variation xy = k

Grade 9 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Read this first
Input–output table
x y
3 15
8 ?
Kira knows y varies directly with x, and y = 15 when x = 3. What is y when x = 8?
Kira knows y varies directly with x, and y = 6 when x = 4. What is y when x = 14?
Kira knows y varies directly with x, and y = 9 when x = 2. What is y when x = 6?
Ren knows y varies directly with x, and y = 8 when x = 5. What is y when x = 15?
Ari knows y varies inversely with x, and y = 15 when x = 4. What is y when x = 6?
Luz knows y varies inversely with x, and y = 18 when x = 2. What is y when x = 12?
7.
Jun fills in a table of a rule, shown in the figure. Is y direct variation, inverse variation or neither?
- Direct variation
- Inverse variation
- Neither
8.
Pia fills in a table of a rule, shown in the figure. Is y direct variation, inverse variation or neither?
- Neither
- Inverse variation
- Direct variation
9.
The rule is y = x/4. Bo meets the rule y = x/4. Is y direct variation, inverse variation or neither?
- Neither
- Inverse variation
- Direct variation
10.
The rule is y = 2x/3. Milo meets the rule y = 2x/3. Is y direct variation, inverse variation or neither?
- Inverse variation
- Neither
- Direct variation

x	y
3	15
8	?

Direct and inverse variation. Every version has 10 questions, and the answer key prints on the second page.

I can find k from one pair for direct variation (y = kx) and for inverse variation (xy = k).
I can find a new value from one pair.
I can tell direct from inverse variation in a table or a rule.

Standard: state-only (A-CED.A.2 and F-LE.A.1b support)

direct variation: y = kx. y ÷ x is the same in every row.

inverse variation: y = k ÷ x, so xy = k. x × y is the same in every row.

constant k: The number that stays the same: y ÷ x for direct, x × y for inverse.

Your child multiplied the two numbers where k is output divided by input.

Your child divided the input by the output, which turns k upside down.

Your child divided where inverse variation multiplies.

Ask: for y = kx, what do you do to y to get k?

Ask: which number goes on top, the output or the input?

Ask: for xy = k, what do you do to x and y to get k?

What is the most common mistake with direct variation y = kx and inverse variation xy = k?

Your child multiplied the two numbers where k is output divided by input.

How can I help my child with direct variation y = kx and inverse variation xy = k?

Ask: for y = kx, what do you do to y to get k?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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