Card 1 of 20
EasyStudy card 1
Prompt
What equation models direct variation?
Answer
\(y=kx\).
MathChapter 14: Rational Expressions
Flashcards
Direct, Inverse, and Joint Variation Flashcards
Twenty recall cards on translating variation, constants, tables, graphs, and powers.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What quotient is constant in direct variation?
Answer
\(y/x=k\), for \(x\ne0\).
Card 3 of 20
EasyStudy card 3
Prompt
What equation models inverse variation?
Answer
\(y=k/x\), equivalently \(xy=k\).
Card 4 of 20
EasyStudy card 4
Prompt
What product is constant in inverse variation?
Answer
\(xy=k\).
Card 5 of 20
EasyStudy card 5
Prompt
What equation models joint variation of \(z\) with \(x,y\)?
Answer
\(z=kxy\).
Card 6 of 20
EasyStudy card 6
Prompt
What graph feature does every direct variation have?
Answer
Its line passes through the origin.
Card 7 of 20
EasyStudy card 7
Prompt
Is \(y=4x+1\) a direct variation?
Answer
No; its nonzero intercept prevents it from passing through the origin.
Card 8 of 20
MediumStudy card 8
Prompt
What does \(k\) represent?
Answer
The constant of variation or proportionality.
Card 9 of 20
MediumStudy card 9
Prompt
How is \(k\) found?
Answer
Substitute one complete set of known corresponding values into the model.
Card 10 of 20
MediumStudy card 10
Prompt
If \(y=5x\), what is \(k\)?
Answer
\(5\).
Card 11 of 20
MediumStudy card 11
Prompt
If \(xy=30\), what kind of variation is present?
Answer
Inverse variation.
Card 12 of 20
MediumStudy card 12
Prompt
If \(y\) varies directly as \(x^2\), what is the model?
Answer
\(y=kx^2\).
Card 13 of 20
MediumStudy card 13
Prompt
If \(y\) varies inversely as \(x^2\), what is the model?
Answer
\(y=k/x^2\).
Card 14 of 20
MediumStudy card 14
Prompt
What happens to direct \(y\) when \(x\) doubles?
Answer
\(y\) doubles, with \(k\) unchanged.
Card 15 of 20
MediumStudy card 15
Prompt
What happens to inverse \(y\) when \(x\) doubles?
Answer
\(y\) is halved, with \(k\) unchanged.
Card 16 of 20
MediumStudy card 16
Prompt
What table test separates direct from inverse variation?
Answer
Check whether \(y/x\) or \(xy\) stays constant.
Card 17 of 20
HardStudy card 17
Prompt
If \(z=kxy\) and both \(x,y\) double, what happens to \(z\)?
Answer
It becomes four times as large.
Card 18 of 20
HardStudy card 18
Prompt
If \(y=k/x^2\) and \(x\) triples, what happens to \(y\)?
Answer
It becomes one ninth as large.
Card 19 of 20
HardStudy card 19
Prompt
Can a negative \(k\) occur in direct variation?
Answer
Yes; the origin-passing line then has negative slope.
Card 20 of 20
HardStudy card 20
Prompt
What is the best safeguard before variation arithmetic?
Answer
Translate the relationship—including every power and named variable—before substituting.
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