What is the slope of the line perpendicular to the line passing through the points \((2,3)\) and \((-1,1)\)?
Answer
Step 2: The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. So, if the slope of the line is \(m\), then the slope of the line perpendicular to it is \(-1/m\). Therefore, the slope of the line perpendicular to the given line is \(-1/(2/3) = -3/2\).
Step 1 ：Step 1: Find the slope of the line passing through the two points using the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1, y_1) = (2,3)\) and \((x_2, y_2) = (-1,1)\), so the slope of the line is \(m = \frac{1 - 3}{-1 - 2} = 2/3\).
Step 2 ：Step 2: The slope of the line perpendicular to the given line is the negative reciprocal of the slope of the given line. So, if the slope of the line is \(m\), then the slope of the line perpendicular to it is \(-1/m\). Therefore, the slope of the line perpendicular to the given line is \(-1/(2/3) = -3/2\).
