CHAPTER VI 



49. The Slope of a Line. The slope of a line could be measured 

 directly by means of the angle it makes with the axis of x, but 

 generally, in cases of plotting, the quantities plotted horizontally 

 and vertically are not taken to the same scale, and therefore we 

 do not get a true representation of the angle of slope. Now this 

 angle can be given in terms of any of its trigonometrical ratios, 

 and we have to consider which of these ratios can be most con- 

 veniently adapted to squared paper work. The tangent is given 

 in terms of the quantities plotted vertically and horizontally, 

 and therefore, if we take the line to form the hypotenuse of a 

 right-angled triangle, then the perpendicular of this triangle can 



FIG. 25. 



be measured by means of the vertical scale, and the base by 

 means of the horizontal scale. Hence the angle of slope of a 

 line can be obtained definitely by means of its tangent. 



To find the slope of a line, take two points A and B (Fig. 25) 

 on the line, as far removed as the limits of the question allow. 

 Make AB the hypotenuse of the right-angled triangle ABC. 



Then the slope of the line = tan 



= AC 

 ~BC 



where AC must be measured on the vertical scale and BC on the 

 horizontal scale. 



50. The Slope of a Curve. The slope of a curve at a given point 

 may be approximately taken as the slope of a very small chord 

 of the curve drawn from that point, and the smaller the chord is 



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