Lecture-13

Lecture-13 - June 20, 2010 Lecture 13: More about lines We...

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Lecture 13: More about lines June 20, 2010 We have shown that every line is the graph of a linear equation (Lecture 9, page 3, Problem 2). We did this by recognizing that given any line, we can Fnd a segment AB of which that line is the perpendicular bisector. The line then consists of those points equidistant from A and B . Using the distance formula, the set of points equidistant from A and B can be described by an equation. That equation simpliFes to a linear one. We did not show yet that the graph of any linear equation is a line. (Problem 3 from Lecture 9 provides one way to do this, but we didn’t do that problem.) This is something so basic and so well-known that you may wonder why we should even bother to ask for an explanation. (You might be wondering, “What will he ask next? Why do we bathe? Why do we dress ourselves?”) The Common Core Standards for eighth grade includes the statement that students should: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation
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Lecture-13 - June 20, 2010 Lecture 13: More about lines We...

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