≡Mathematics EN 9th grade: Direct Proportionality Function
1. Definition
A direct proportionality function is a function where two quantities vary proportionally.
👉 If one increases, the other also increases (or decreases proportionally).
Its general form is:
\( y = kx \)
where:
𝑘 is the constant of proportionality
𝑥 is the independent variable
𝑦 is the dependent variable
✔ Example:
\( y = 2x \)
2. Meaning of the constant 𝑘
The constant 𝑘 indicates the ratio between 𝑦 and 𝑥:
\( k = \frac{y}{x} \)
✔ Example:
If 𝑥 = 3 and 𝑦 = 6 :
\( k = \frac{6}{3} = 2 \)
👉 Therefore, the function is 𝑦 = 2 𝑥
3. Characteristics of the function
✔ Passes through the origin:
\( (0,0) \)
✔ The graph is a straight line
✔ The slope is equal to 𝑘
✔ Direct proportional relationship between 𝑥 and 𝑦
4. Graphical Representation 👉 The graph is a straight line that passes through the origin.
Each point satisfies: \( y = kx \) ✔ Example of points:
If 𝑦 = 2𝑥: \( (1,2), (2,4), (3,6) \) 5. Determining the function
If we know a pair of values ( 𝑥, 𝑦 ), we can find 𝑘
✔ Example:
If 𝑥 = 4 and 𝑦 = 12: \( k = \frac{12}{4} = 3 \) 👉 Function: \( y = 3x \) 6. Check if it's direct proportionality
A function is directly proportional if:
\( \frac{y}{x} = k \) \text{ (constant)}
✔ Example:
𝑥 - 𝑦
1 - 2
2 - 4
3 - 6
\( \frac{2}{1} = \frac{4}{2} = \frac{6}{3} = 2 \)
👉 It is directly proportional
QUICK TIPS FOR THE EXAM
✔ General form:
\( y = kx \)
✔ Always passes through the origin ( 0, 0 )
✔\( k = \frac{y}{x} \)
✔ Graph → straight line
✔ Ratio \( \frac{y}{x} \) constant
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