Write the equation of the line that passes through the given points. \[ \left(\frac{1}{8}, \frac{1}{2}\right) \text { and }\left(\frac{3}{8}, 0\right) \] The equation of the line is \( \square \) (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
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To find the equation of the line passing through the points \(\left(\frac{1}{8}, \frac{1}{2}\right)\) and \(\left(\frac{3}{8}, 0\right)\), we start by calculating the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - \frac{1}{2}}{\frac{3}{8} - \frac{1}{8}} = \frac{-\frac{1}{2}}{\frac{2}{8}} = \frac{-\frac{1}{2}}{\frac{1}{4}} = -2. \] Now that we have the slope, we can use the point-slope form of the line equation \(y - y_1 = m(x - x_1)\). Using the point \(\left(\frac{1}{8}, \frac{1}{2}\right)\): \[ y - \frac{1}{2} = -2\left(x - \frac{1}{8}\right). \] Distributing the slope: \[ y - \frac{1}{2} = -2x + \frac{2}{8} = -2x + \frac{1}{4}. \] Adding \(\frac{1}{2}\) to both sides to solve for \(y\): \[ y = -2x + \frac{1}{4} + \frac{1}{2} = -2x + \frac{1}{4} + \frac{2}{4} = -2x + \frac{3}{4}. \] Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = -2x + \frac{3}{4}}. \]
