To determine if the function \( f(x) = \frac{1}{2}x - 6 \) represents a linear relationship, we can examine its form.
A function is considered linear if it can be expressed in the standard form \( f(x) = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
In this case, the function \( f(x) = \frac{1}{2}x - 6 \) can be rewritten with:
- \( m = \frac{1}{2} \) (the coefficient of \( x \)),
- \( b = -6 \) (the constant term).
Since \( f(x) \) fits the form \( f(x) = mx + b \), we can conclude that it is indeed a linear relationship. The graph of this function would be a straight line with a slope of \( \frac{1}{2} \) and a y-intercept at \( (0, -6) \).