Problem

Given the equations of two lines, \(y = 2x + 3\) and \(y = mx + 4\), find the value of \(m\) that will make the two lines perpendicular.

Answer

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Answer

Solving the above equation for \(m\), we get \(m = -1/2\).

Steps

Step 1 ：The slope of a line given by the equation \(y = mx + c\) is \(m\). So, the slope of the first line is \(2\).

Step 2 ：If two lines are perpendicular, the product of their slopes is \(-1\). Therefore, \(m * 2 = -1\).

Step 3 ：Solving the above equation for \(m\), we get \(m = -1/2\).

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