To determine which of the given equations represents a linear function, we can analyze each one:
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\(2x - 4 = 6\): This equation can be simplified to find \(x\).
- Adding 4 to both sides yields \(2x = 10\),
- Dividing by 2 gives \(x = 5\).
- This is not a linear function because it does not define \(y\) in terms of \(x\).
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\(x = -2\): This equation represents a vertical line at \(x = -2\).
- It does not represent a function in the traditional sense (where each \(x\) has a single \(y\)), but it can be considered a linear equation.
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\(y = \frac{1}{2}x^2\): This equation represents a parabolic function (quadratic function), not a linear function.
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\(y = \frac{2}{3}x + 4\): This is the standard form of a linear equation (in slope-intercept form \(y = mx + b\)), where \(m = \frac{2}{3}\) (the slope) and \(b = 4\) (the y-intercept).
From this analysis, the equation that represents a linear function is:
\(y = \frac{2}{3}x + 4\).