Proportionality Calculator

Relationship

Exponent n (power variation)2 for "varies as the square", -2 for an inverse-square law.

Known xThe first term: a in the proportion a/b = c/x, or the first part of the ratio a : b.

Known yThe second term: b in the proportion a/b = c/x, or the second part of the ratio a : b.

Known z (joint variation)

Constant of variation k (if already known)Supply this instead of a known x and y pair.

What do you want to find?

New xThe third term: c in the proportion a/b = c/x. Leave it blank in ratio mode to just simplify a : b.

New y

New z (joint variation)

Answer

Direct and Inverse Variation Calculator

Constant of variation k

x in the second situation

y in the second situation

Equation of variation

y = 4x

What the relationship means

y varies directly with x: double x and y doubles.

Worked out from OpenStax, College Algebra 2e §5.8 "Modeling Using Variation" — direct variation y = kx^n, inverse variation y = k/x^n and joint variation.

How this is worked out

4 steps

Substitute the known pair into y = kx:
12 = k x 3^1, so k = 12 / 3 = 4
Equation of variation: y = 4x
Substitute x = 7: y = 4 x 7^1 = 28

Results are general information, not financial, tax, legal, medical or engineering advice.