Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Vertical Change Slope – is the ratio of the vertical change to the horizontal change of two points. Section 4.4 – Find Slope and Rate of Change Formula of Slope : Slope (m) == Horizontal Change _______________ Change in y = Change in x __________ Δ y = Δ x ___ y 2 – y 1 x 2 – x 1 ______

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 1 Find the slope of the line shown. Section 4.4 – Find Slope and Rate of Change Write formula for Slope : Let (x 1, y 1 ) = (-2, -2) and (x 2, y 2 ) = (6, 4) Substitute: Simplify: The slope of the line is

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 2 Find the slope of the line shown. Section 4.4 – Find Slope and Rate of Change Write formula for Slope : Let (x 1, y 1 ) = (-2, 2) and (x 2, y 2 ) = (3, 1) Substitute: Simplify: The slope of the line is

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 3 Find the slope of the line shown. Section 4.4 – Find Slope and Rate of Change Write formula for Slope : Let (x 1, y 1 ) = (-2, -1) and (x 2, y 2 ) = (4, -1) Substitute: Simplify: The slopes of all horizontal lines are ZERO The line is horizontal The slope of the line is

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 4 Find the slope of the line shown. Section 4.4 – Find Slope and Rate of Change Write formula for Slope : Let (x 1, y 1 ) = (-3, 1) and (x 2, y 2 ) = (-3, -3) Substitute: Simplify: The slopes of all vertical lines are UNDEFINED The line is vertical The slope of the line is undefined

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Rate of Change – compares a change in one quantity to a change in another quantity. Example # 5 The table shows the cost to paint a house for a given number of hours. Find the rate of change in cost with respect to time. Rate of Change = Section 4.4 – Find Slope and Rate of Change Time (hours)468 Cost ($) Change in Cost Change in Time ______________ Trial 1 := $22.50 per hour Trial 2 := $22.50 per hour Trial 3 := $22.50 per hour The trials confirm, the Rate of Change is constant. The rate of change is $22.50 per hour.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 6 The graph shows the number of computer games sold day 1, day 4, day 7, and day 9 of a sale. Describe the rates of change in sales with respect to time. Find the rates of change using the slope formula. Section 4.4 – Find Slope and Rate of Change Rate of Change = Change in Computers Sold Change in Days ______________________

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Example # 6 (con’t) - Section 4.4 – Find Slope and Rate of Change Days := 23 computers sold per day. Days := 10 computers sold per day. Days := -21 computers sold per day. Rate of Change Describe the rates of change in sales with respect to time. Days : Sales increased at a fast rate. Days : Sales increased at a slower rate. Days : Sales decreased at a moderate rate.

Chapter 4 – Graphing Linear Equations and Functions Algebra I A - Meeting 24 Homework # 17 pg 239 – 241 # 3 – 16 all; # 19; # 21 – 26 all; # 36; #39 Section 4.4