121616949-math.18

121616949-math.18 - 4 Chapter 1 Analytic Geometry relation...

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4 Chapter 1 Analytic Geometry relation says that “between the point ( x 1 , y 1 ) and any other point ( x, y ) on the line, the change in y divided by the change in x is the slope m of the line.” It is possible to find the equation of a line between two points directly from the relation ( y - y 1 ) / ( x - x 1 ) = ( y 2 - y 1 ) / ( x 2 - x 1 ), which says “the slope measured between the point ( x 1 , y 1 ) and the point ( x 2 , y 2 ) is the same as the slope measured between the point ( x 1 , y 1 ) and any other point ( x, y ) on the line.” For example, if we want to find the equation of the line joining our earlier points A (2 , 1) and B (3 , 3), we can use this formula: y - 1 x - 2 = 3 - 1 3 - 2 = 2 , so that y - 1 = 2( x - 2) , i.e., y = 2 x - 3 . The slope m of a line in the form y = mx + b tells us the direction in which the line is pointing. If m is positive, the line goes into the 1st quadrant as you go from left to right. If m is large and positive, it has a steep incline, while if m is small and positive, then the line has a small angle of inclination. If m
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