To find the slope of the line that is perpendicular to the line given by the equation \(2x - 3y = 8\), we first need to determine the slope of that line.
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Rearrange the equation into slope-intercept form (y = mx + b): \[ 2x - 3y = 8 \] Subtract \(2x\) from both sides: \[ -3y = -2x + 8 \] Now, divide by \(-3\): \[ y = \frac{2}{3}x - \frac{8}{3} \] From this, we can see that the slope \(m\) of the line is \( \frac{2}{3} \).
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Find the slope of the perpendicular line: The slope of a line perpendicular to another is the negative reciprocal of the original slope. Thus, we take the negative reciprocal of \( \frac{2}{3} \): \[ \text{Perpendicular slope} = -\frac{1}{\frac{2}{3}} = -\frac{3}{2} \]
So, the slope of the line perpendicular to \(2x - 3y = 8\) is \(-\frac{3}{2}\).
The correct answer from the options provided is: A. negative 3-halves.
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