This episode introduces the concept of slope. Beginning in the Sierra mountains with an investigation of what it means for a road to have a 5% grade, we quickly move to an understanding of the terms rise and run and the definition of slope as the ratio of rise to run. We then look at how slope triangles can be used to measure the rise and run and determine the slope of a line. From here we look at how the formula for slope enables us to find the change in y (the rise) and the change in x (the run) given two ordered pairs. After quite a bit of practice using the formula for slope, we are ready to make some generalizations regarding the slope of a line. First we look at how the direction of a line (uphill, downhill, horizontal and vertical) corresponds with the value for slope (positive, negative, zero and undefined). Then we look at how the absolute value of the slope of a line tells you how steep a line is (lines with slopes that are close to zero are close to horizontal and lines get steeper as their slopes get farther from zero). Finally, we learn how to draw a line through a given point with a given slope.
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