Rate of Change & Slope Lesson 33

Objectives HSF-LE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. HSF-IF.6: Calculate and interpret rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Example; find the rate of change Is the rate of change constant or not? If so, what is the rate of change? x y 1 10 2 17 3 24 4 31 Yes, the rate of change does seem to be constant. +1 +7 +1 +7 +1 +7 17 - 10 7 = = 7 2 - 1 1 R.o.C = m = 7

Example; find the rate of change Is the rate of change constant or not? If so, what is the rate of change? x y 1 10 2 17 3 22 4 29 No, the rate of change is not constant. The y values increase at different intervals. +1 +7 +1 +5 +1 +7

Example: Finding the Slope of a Line Given Two Points Find the slope of the line through (–1, 1) and (2, –5). Let (x1, y1) be (–1, 1) and (x2, y2) be (2, –5). Use the slope formula. Put in what you know. Simplify The slope of the line is –2.

Example; find the slope of the line Let (x1, y1) be (–2, 0) and (x2, y2) be (2, 3). Use the slope formula. 3 - 0 = Put in what you know. 2 - -2 3 = Simplify 4 The slope of the line is ¾.

Example; Horizontal or Vertical Any Horizontal line will have an equation: y = “some number” y = 4 Any Vertical line will have an equation: x = “some number” x = -3

#33: Rate of Change & Slope Questions? Summarize Notes Homework Google Classroom Quiz