Question

Which equation represents a direct linear variation?

a) y = 1/x
b) y = x - 3
c) y = x^2

Answer 1

The equation representing a direct linear variation is b) y = x - 3.

So. the correct statement is B.

Step-by-step explanation:

Direct linear variation refers to a linear relationship between two variables expressed in the form
`\(y = mx + b\)` where
`\(m\)` is the slope and
`\(b\)` is the y-intercept.

In the given options only
`\(y = x - 3\)` (option b) follows this format, making it indicative of direct linear variation. The coefficient of
`\(x\)` is 1 denoting the slope and the constant term is -3 representing the y-intercept.

`\(y = 1/x\)` represents an inverse variation as the dependent variable is inversely proportional to
`\(x\)`. This is distinct from direct linear variation. Additionally
`\(y = x^2\)` is a quadratic equation, which does not exhibit a linear relationship between
`\(x\)` and
`\(y\)`.

Understanding these distinctions in mathematical expressions is crucial for accurately interpreting relationships between variables in various contexts from physics to economics.

Recognizing direct linear variation aids in constructing appropriate models for real world scenarios where variables exhibit a constant rate of change. In summary aligns with the characteristics of direct linear variation making it the correct choice.

So. the correct statement is B.