UM CURSO DE CALCULO GUIDORIZZI PDF
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The fact that the line is straight means that the rate of change is constant. Figure 8 shows several lines labeled with their slopes. Notice that lines with positive slope slant upward to the right,whereas lines with negative slope slant downward to the right.
Notice also that the steepest lines are the ones for which the absolute value of the slope is largest,and a horizontal line has slope 0. A point with lies on this line if and only if the slope of the line through and is equal to ; that is,.
Therefore,it is an equation of the given line. Point-Slope Form of the Equation of a Line An equation of the line passing through the point and having slope is.
Guidorizzi – Um Curso de Cálculo – Volume 1
Suppose a nonvertical line has slope and -intercept. See Figure 9. This meansit intersects the -axis at the point ,so the point-slope form of the equation of the line, with and ,becomes.
In particular,if a line is horizontal,its slope is ,so its equation is ,where is the -intercept see Figure A vertical line does not have a slope,but we can write its equation as ,where is the -intercept,because the -coordinate of every point on the line is.
Compare this inequality with the equation ,which represents a line with slope and -intercept.
We see that the given graph consists of points whose -coordinates are largerthan those on the line. Thus,the graph is the region that lies abovethe line,as illustrated in Figure 1. Slopes can be used to show that lines are parallel or perpendicular. The following facts are proved,for instance,in Precalculus: Parallel and Perpendicular Lines 1.
Two nonvertical lines are parallel if and only if they have the same slope. Two lines with slopes and are perpendicular if and only if ; that is,their slopes are negative reciprocals:. Why not share! Embed Size px. Start on. Show related SlideShares at end.
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