This chapter covers determining and calculating the slope of a line.
STATE the definition of the following terms:
Given the equation, CALCULATE the slope of a line.
Given the graph, DETERMINE the slope of a line.
Many physical relationships in science and engineering may be expressed by plotting a straight
line. The slope(m), or steepness, of a straight line tells us the amount one parameter changes for
a certain amount of change in another parameter.
For a straight line, slope is equal to rise over run, or
change in y
change in x
Consider the curve shown in Figure 11. Points P1 and P2 are any two different points on the
line, and a right triangle is drawn whose legs are parallel to the coordinate axes. The length of
the leg parallel to the x-axis is the difference between the x-coordinates of the two points and
is 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 containing
points (1,3) and (3,7) in the second part of the figure. The difference between the x-coordinates
is Dx = 3-1 = 2. The difference between the y-coordinates is Dy = 7-3 = 4. The ratio of the
differences, Dy/Dx, is the slope, which in the preceding example is 4/2 or 2. It is important to
notice 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 on
the inclination of the line, m = rise [vertical (y-axis) change] ÷ run [horizontal (x-axis) change].