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Intercepts of a Line Passing Through the Origin
When a straight line passes directly through the origin of a rectangular coordinate system, its x-intercept and y-intercept are exactly the same point: . This occurs because the origin is the unique location where both the x-axis and the y-axis intersect, meaning the line crosses both axes simultaneously. For equations representing such lines, setting results in and setting results in . Consequently, the standard method of finding two distinct intercepts yields only a single point, requiring the identification of additional solution points to properly graph the line.
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Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
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