Direct and Inverse Proportion

Proportion written as an equation rather than worked as a recipe — which is what lets you answer questions the unitary method cannot reach.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ต่อยอดจาก ม.1 บทที่ 7 อัตราส่วนและสัดส่วน
Common Core (US): 7.RP, 8.F
Cambridge: Lower Secondary Stage 9 — Number: ratio and proportion

4.1 Direct proportion as an equation

Direct proportion

y \propto x ⟺ y = k x

$k$ is the constant of proportionality. Finding $k$ once answers every later question about the same relationship.

The method

1Write the relationship as $y = k x$
2Substitute the pair of values you were given and solve for $k$
3Write the equation out with $k$ filled in
4Use it to answer the question

ตัวอย่าง

$y$ is directly proportional to $x$ , and $y = 45$ when $x = 9$ . Find $y$ when $x = 14$ .

วิธีทำ

1. $y = k x$ , so $45 = 9 k$ and $k = 5$
2.The relationship is $y = 5 x$
3. $y = 5 \times 14$

ตอบ $y = 70$

ทำไมถึงเป็นแบบนั้น

The unitary method from Stage 7 does the same job for simple cases. The equation earns its place when the relationship is not linear — $y \propto x^{2}$ has no "one unit" to scale from, but $y = k x^{2}$ works exactly as before.

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