Writing Equations of Parallel and Perpendicular Lines

① This interactive GeoGebra example dynamically generates random points and lines, prompting students to write equations for lines that are parallel or perpendicular to a given line through a given point. ② Core mathematical concepts include slope of a line, equal slopes for parallel lines, negative reciprocal slopes for perpendicular lines, and point-slope/slope-intercept forms of linear equations. ③ Construction highlights: commands such as Random and RandomElement generate random points and slopes, Line constructs the base line, FractionText displays slopes as fractions, Sequence builds answer choices, Textfield and InputBox allow student input, Union merges lists, Denominator handles fractions, and a button (button1) triggers new problems. ④ Suitable for upper middle school or high school algebra/geometry classes, this resource serves both as a teacher demonstration tool and a self-paced practice environment, reinforcing the algebraic conditions for parallelism and perpendicularity in coordinate geometry.