Calculus 2nd Edition Rogawski

14 CHAPTER 1 PRECALCULUS REVIEW
The slope m measures the rate of change of y with respect to x. In fact, by writing
y = mx
we see that a one-unit increase in x (i.e., x = 1) produces an m-unit change y in y. For
example, if m = 5, then y increases by five units per unit increase in x. The rate-of-change
interpretation of the slope is fundamental in calculus. We discuss it in greater detail in
Section 2.1.
Graphically, the slope m measures the steepness of the line y = mx + b. Figure 2(A)
shows lines through a point of varying slope m. Note the following properties:
• Steepness: The larger the absolute value |m|, the steeper the line.
• Negative slope: If m0 and decreasing if m