AMSCO'S Geometry. New York - Rye High School

The Slope of a Line 2918-1 THE SLOPE OF A LINEIn the coordinate plane, horizontal and vertical lines are used as reference lines.Slant lines intersect horizontal lines at acute and obtuse angles. The ratio thatmeasures the slant of a line in the coordinate plane is the slope of the line.Finding the Slope of a LineThrough two points, one and only one line can be drawn. In the coordinateplane, if the coordinates of two points are given, it is possible to use a ratio todetermine the measure of the slant of the line. This ratio is the slope of the line.Through the points A(1, 2) and B(2, 7),AB gyis drawn. Let C(2, 2) be the point at whichB(2, 7)the vertical line through B intersects the horizontalline through A. The slope of AB is theratio of the change in vertical distance, BC, tothe change in horizontal distance, AC. Since Band C are on the same vertical line, BC is thedifference in the y-coordinates of B and C.Since A and C are on the same horizontal line,AC is the difference in the x-coordinates of Aand C.change in vertical distanceslope of AB 5 change in horizontal distance5 ACBC5 7 2 (22)2 2 (21)5 9 35 3This ratio is the same for any segment of the line AB g. Suppose we changethe order of the points (1, 2) and (2, 7) in performing the computation. Wethen have:slope of BA 5change in vertical distancechange in horizontal distance5 CBCA5 (22) 2 7(21) 2 25 29235 3A(1, 2)The result of both computations is the same. When we compute the slope ofa line that is determined by two points, it does not matter which point is consideredas the first point and which the second.11O1xC(2, 2)