To find the equation of the line that passes through the points \((0, 35)\) and \((-12, 34)\), we need to determine the slope of the line and then use the point-slope form of the equation.
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Calculate the slope (m): The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (0, 35)\) and \((x_2, y_2) = (-12, 34)\): \[ m = \frac{34 - 35}{-12 - 0} = \frac{-1}{-12} = \frac{1}{12} \]
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Use the point-slope form: The point-slope form of the equation of a line is: \[ y - y_1 = m(x - x_1) \] We'll use the point \((0, 35)\): \[ y - 35 = \frac{1}{12}(x - 0) \] Simplifying this gives: \[ y - 35 = \frac{1}{12}x \] \[ y = \frac{1}{12}x + 35 \]
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Convert to slope-intercept form (if necessary): The equation is already in slope-intercept form \(y = mx + b\), where \(m = \frac{1}{12}\) and \(b = 35\).
None of the provided options directly match this equation. Thus, it seems that there might be a miscommunication in the options provided.
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