To find the equation of the linear function that passes through the points (0, 1/2) and (1, 1/4), we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Calculate the slope (m): The slope \( m \) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 1/2) \((x_1, y_1)\) and (1, 1/4) \((x_2, y_2)\): \[ m = \frac{\frac{1}{4} - \frac{1}{2}}{1 - 0} = \frac{\frac{1}{4} - \frac{2}{4}}{1} = \frac{-\frac{1}{4}}{1} = -\frac{1}{4} \]
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Use the y-intercept (b): Since the line passes through (0, 1/2), we can see that the y-intercept \( b = \frac{1}{2} \).
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Write the equation: Plugging the slope and y-intercept into the slope-intercept form: \[ y = -\frac{1}{4}x + \frac{1}{2} \]
Thus, the equation representing the function is: \[ y = -\frac{1}{4}x + \frac{1}{2} \]