AlgebraSLOPESSLOPESThis chapter covers determining and calculating the slope of a line.EO 1.14 STATE the definition of the following terms:a. Slopeb. InterceptEO 1.15 Given the equation, CALCULATE the slope of a line.EO 1.16 Given the graph, DETERMINE the slope of a line.Many physical relationships in science and engineering may be expressed by plotting a straightline. The slope(m), or steepness, of a straight line tells us the amount one parameter changes fora certain amount of change in another parameter.SlopeFor a straight line, slope is equal to rise over run, orsloperiserunchange in ychange in xDyDxy_{2}y_{1}x_{2}x_{1}Consider the curve shown in Figure 11. Points P1 and P2 are any two different points on theline, and a right triangle is drawn whose legs are parallel to the coordinate axes. The length ofthe leg parallel to the x-axis is the difference between the x-coordinates of the two points andis called "Dx," read "delta x," or "the change in x." The leg parallel to the y-axis has length Dy,which is the difference between the y-coordinates. For example, consider the line containingpoints (1,3) and (3,7) in the second part of the figure. The difference between the x-coordinatesis Dx = 3-1 = 2. The difference between the y-coordinates is Dy = 7-3 = 4. The ratio of thedifferences, Dy/Dx, is the slope, which in the preceding example is 4/2 or 2. It is important tonotice that if other points had been chosen on the same line, the ratio Dy/Dx would be the same,since the triangles are clearly similar. If the points (2,5) and (4,9) had been chosen, then Dy/Dx= (9-5)/(4-2) = 2, which is the same number as before. Therefore, the ratio Dy/Dx depends onthe inclination of the line, m = rise [vertical (y-axis) change] ÷ run [horizontal (x-axis) change].Rev. 0 Page 85 MA-02

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