Prove and use slope criteria for parallel and perpendicular lines.
Write an equation of a line parallel to a given line through a point
Problem
Write the equation of the line parallel to \(y=2x+5\) that passes through \((3,1)\).
Big Picture
What this problem is really about
A parallel-through-a-point problem separates direction from position: keep the given line’s slope, but do not copy its intercept. Insert the new point into point-slope form or into y equals mx plus b, solve for the remaining constant, and verify both the slope and point afterward.
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