Average Rate of Change.

Slides:

Advertisements

Similar presentations

Finding the Slope of a Line From Two Points

Advertisements

Proving Average Rate of Change

Introduction In previous lessons, we have found the slope of linear equations and functions using the slope formula,. We have also identified the slope.

3.3 Find Slope and Rate of Change Objective: Students will be able to find the slope of a line and interpret slope as a rate of change.

I can find the slope of a line from a table or graph.

Warm-up Find the slope y x Run=6-2=4 Rise=3-1=2 = (2,1) (6,3)

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Slope.

Drill #57 Write an equation in function notation for the following relations: {(-1, 6), (0, 3), (1,0)} XY XY

Constant Rate of Change and Slope 9.3. Rate of Change Rate of Change: describes how a quantity changes in relation to another Constant Rate of Change:

Section 3.1 Linear Functions and Their Properties.

Warm up 1.a. Write the explicit formula for the following sequence -2, 3, 8, 13,… b. Find a 10 2.a. Write the recursive formula for the following sequence.

Warm up Find the domain and range of the following graphs.

5-1B Rate of Change Warm-up (IN) Learning Objective: to understand that slope is the rate of change of one quantity relative to another and to be able.

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.

Warm up 1.What is the tenth term of a n = 2n + 3? 2. What is the Domain: Range: x – ints: y – int:

0-6 Writing Equations in Point- Slope Form. Slope Formula y 1 – y 2 x 1 – x 2 Forms of lines Point-slope form: y – y 1 = m (x - x 1 )

Ch. 5 Vocabulary ) Rate of change 2.) slope.

Rate of change and Slope Rise over Run The change of the rise over the change of the run.

Section 2.2 – Linear Equations in One Variable

Rate of Change and Slope

Lesson 3.5 Essential Question: How can you describe the graph of the equation y=mx+b? `Objectives: Finding the slope of a line Finding the slope of a line.

(exponential functions)

Ex 2: Graph the line with slope 5/2 that passes through (-1, -3)

Warm up What is the tenth term of an = 2n + 3?

Slope Slope is the steepness of a straight line..

Characteristics of Functions

Warm up 1.a. Write the explicit formula for the following sequence

Rate of Change and Slope

Lesson 3.5 Average Rate of Change (exponential functions)

5-Minute Check Lesson 1-3A

College Algebra Chapter 2 Functions and Graphs

Graphing Linear Equations in Slope-Intercept Form

WARM UP Determine the constant rate of change and determine if it linear or not?

Equations of Lines in the Coordinate Plane

4.5 Point-Slope form of a linear equation

Introduction To Slope.

MAT 150– Algebra Class #4 Today’s Topics: Writing Equations of Lines

Rate of Change and Slope

Objectives Find rates of change and slopes.

Slope How did we define slope yesterday?

Warm Up 1. Find the x- and y-intercepts of 2x – 5y = 20.

12/1/2018 Lesson 1-3 Formulas Lesson 1-3: Formulas.

Section 1.2 Straight Lines.

Slope = m = rate of change

Slope Determine whether the slope is positive, negative, Zero, or undefined.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Characteristics of Functions

Average Rate of Change.

A _________________ is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable. Rate of Change.

Average Rate of Change.

Average Rate of Change.

Average Rate of Change.

Rate of Change and Slope

Pre-Calculus Go over homework End behavior of a graph

Warm up What is the tenth term of an = 2n + 3?

Average Rate of Change.

Graph Each Equation Using the Intercepts

Rate of Change and Slope

Warm up What is the tenth term of an = 2n + 3? 23

5-1 Rate of Change and Slope

Warm up What is the tenth term of an = 2n + 3?

Warm up What is the tenth term of an = 2n + 3? What is the Domain:

Perpendicular and Parallel Lines

Tell whether the slope is positive or negative. Then find the slope.

Average Rate of Change.

Average Rate of Change.

COURSE 3 LESSON 3-3 Understanding Slope

5.1 Rate of Change and Slope

Warm up What is the tenth term of an = 2n + 3?

Presentation transcript:

Average Rate of Change

Rate of Change A ratio that describes how one quantity changes as another quantity changes Slope can be used to describe it

Rate of Change Positive – increases over time Negative – decreases over time Zero- doesn’t change over time Horizontal movement Undefined - vertical movement

Rate of Change Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

Average Rate of Change using function notation

Ex 1 Find the Average Rate of Change f(x) = 2x2 – 3 from [2, 4].

Ex 2 Find the Average Rate of Change f(x) = -4x + 10 from [-1, 3]. m = -4

A. Find the rate of change from day 1 to 2. Ex 3 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 Days (x) Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5 121 6 192 B. Find the rate of change from day 2 to 5.

Ex 4 Find the Average Rate of Change Households in Millions f(x) In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. Year (x) Households in Millions f(x) 2008 66 2009 61 2010 56 2011 51 m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.