Prove and use slope criteria for parallel and perpendicular lines.
Write an equation of a line perpendicular to a given line through a point
Problem
Write the equation of the line perpendicular to \(y=2x+5\) that passes through \((4,1)\).
Big Picture
What this problem is really about
Build the line in two stages: first replace the given slope with its negative reciprocal, then use the required point to determine position. After simplifying the equation, check that the two slopes multiply to negative one and that substituting the point satisfies the equation.
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