To find the equation of the linear function that passes through the points (0, 1/2) and (1, 1/4), we can start by calculating the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where \((x_1, y_1) = (0, 1/2)\) and \((x_2, y_2) = (1, 1/4)\):
\[ m = \frac{1/4 - 1/2}{1 - 0} = \frac{1/4 - 2/4}{1} = \frac{-1/4}{1} = -\frac{1}{4} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point (0, 1/2) and the slope \(-1/4\):
\[ y - \frac{1}{2} = -\frac{1}{4}(x - 0) \]
This simplifies to:
\[ y - \frac{1}{2} = -\frac{1}{4}x \]
Now, add \(\frac{1}{2}\) to both sides to solve for \(y\):
\[ y = -\frac{1}{4}x + \frac{1}{2} \]
Thus, the equation can be rewritten as:
\[ y = -\frac{1}{4}x + \frac{1}{2} \]
Looking at the response options provided, we find that the correct equation that represents the function is:
B. \( y = -\frac{1}{4}x + \frac{1}{2} \)