Higher only · proportion equations
Proportion with
equations. Find k,
then use it.
y ∝ x means y = kx
the symbol ∝ means —
Proportional to
y ∝ x becomes y = kx
swap ∝ for “= k ×”, every time
step 1 of 4
Write the equation
1. Direct: k times x.
2. Inverse: k divided by x.
✓ k is the constant of proportionality
y ∝ x direct
y = kx
y ∝ 1x inverse
y = kx
step 2 of 4
Find k
1. Put in the pair of values you are given.
2. Solve for k. Rewrite the equation.
✓ Now it works for any value
y ∝ x, and y = 12 when x = 3
12 = k × 3
k = 4
y = 4x
step 3 of 4
Use it
1. Substitute to find y.
2. Or solve to find x.
✓ Same equation, both directions
y = 4x
x = 7: y = 4 × 7 = 28
y = 50: 50 = 4x, so x = 12.5
step 4 of 4
Squares and inverses
1. Whatever follows ∝ goes after the k.
2. Square x before multiplying.
✓ Inverse: multiply to find k
y ∝ x2: y = kx2
y = 20, x = 2: 20 = 4k, k = 5
y ∝ 1x: y = 6 when x = 4
6 = k4, so k = 24
proportion equations —
Find k
substitute the given pair
Use
rewrite with k, then substitute
Three marks: equation, k, answer.
Show all three.
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