Applications of Rates and Proportional Reasoning: Rate of Change Today you will learn to: Calculate the rate of change from a graph Calculate the slope.

Slides:

Advertisements

Similar presentations

4 minutes Warm-Up 1) Find the slope of the line containing the points (-1,12) and (5,-6). 2) Identify the slope and y-intercept for the line y = -5x.

Advertisements

Warm Up Determine the anti-derivative. Then differentiate your answer to check your work Evaluate the definite integral: 3.

5 Minute Check Find the equation for the following graphs. Complete in your notes

Six students brought money for the school field trip to Flagler’s Museum. Their teacher plotted the smallest and largest amounts of money brought by the.

Warm-up 1.) Write 25% as a fraction in lowest terms and as a decimal. 2.) Make an input-output table for the function , use the values -2, -1, 0, 1, 2,

Topic: Position-Time Graphs Unit 1: Chapter 1 and 2.

EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles.

5-4 Rates of Change and Slope Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

REMEMBER: A number can be negative or positive as shown in the number line below: Negative Numbers (-) Positive Numbers (+)

Relationships. Direct Proportion Two quantities are directly proportional if an increase in one causes an increase in the other. Example: y = 2 x Example:

HOW TO ADD INTEGERS REMEMBER:

Average Speed Practice Problems

5.3 Rate of Change and Slope 5.4 The Slope Formula

Velocity Time Graph.

Unit Rate and proportional reasoning

Measuring Motion Chapter 11. What is Motion? Motion is changing position along a certain path. In the first part of physical science, we have 2 goals:

Chapter 7 – Systems of Linear Equations and Inequalities

Warm-Up Graph each point in the same coordinate plane. 1) A(1,400) 4 minutes 2) B(3,300) 3) C(6,150)4) D(8,50) 5) Suppose that a line were drawn to connect.

1-4 Adding Integers Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

1-5 Adding Integers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

Measuring Motion  Speed  Velocity  Acceleration.

P ATTERNS AND F UNCTIONS (L INEAR AND N ON - LINEAR ) Lessons 4-2 and 4-3.

Warm Up # 3 Quarterly Assessment 3 Take out your Make Up QA – work on them quietly Work on your homework if you are finished.

Grade 4 Chapter 13 & 14. Brooke ran the 200 meter in twenty eight and six hundredths seconds. How is this number written? a b c d.

Target: Recognize a graph given words and explain the meaning of graphs.

Copyright 2006 BrainyBetty.com ALL RIGHTS RESERVED. October 19, 2011 By the end of today: –I will be able to find slope from a graph. Warm-up: Graph y.

Introduction The average running speed of a human being is 5–8 mph. Imagine you set out on an 8-mile run that takes you no longer than 1 hour. You run.

Do Now Describe your position in the classroom using a reference point and a set of reference directions. Record your response in your science journal.

Warm-up During a five day work week, the stock market dropped sixty-five points. Find the average daily change for each day of the week.

Solving Algebraic Equations Equation: = 5 Solving Algebraic Equations Equation: = = 2 2 = 2.

STARTER During a road trip, in 6 hours you travel 300 miles. What is your average velocity? Average Velocity = distance travelled/time taken = 300 miles/6.

1. Use the following points from a graph to determine the slope. (2,15), (8, 45) 2. What does it mean for a line to be linear? 3. On a distance/time graph,

Exam #4 Review. 1.Snyder students drove 700 km from PA to MA. They left at 7 am and arrived in MA at 3 pm. The students visited an aquarium for 2 hours.

Chapter 4 – Graphing Linear Equations 4.4 – The Slope of a Line.

Motion Review. What is the difference between an independent and dependent variable?

Time (days)Distance (meters) The table shows the movement of a glacier over six days.

TOC: Speed= Distance/Time 11/9/2015

Revisiting Slope Lesson 3.2.

Bellwork-- Graph Solutions Intro to Systems of Equations and Graphing MFCR Lesson

Kawameeh 8 th Grade Science.  Reference Point - The starting point you chose to describe the location, or position of an object. Position - An object’s.

CHAPTER 4 TEST REVIEW v Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Question.

DO NOW – 5 th period V: 0 Monday 11/9 On your post-it note, answer the following question. Use the sentence stem to answer in a complete sentence. What.

2. Four gallons of gasoline cost $ What is the price per gallon?

Warm up Problem An athlete sprints 50.0 m to the right in 6.00 s, stops and then walks back to the starting line in 40.0 s. Determine a) the average velocity.

The Slope of a Line. Important things about slope… Slope is the change in y over change in x. Slope is represented by the letter m Vertical line has NO.

Average and Rate Problems with Multiple Steps LESSON 55POWER UP JPAGE 386.

Example 2 Writing an Algebraic Expression You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles per hour.

Warm-Up: September 15, 2015 Using the graph and line of best fit from yesterday’s class, estimate the length of the spring when 50 g is hung from it.

5.3: Position, Velocity and Acceleration. Warm-up (Remember Physics) m sec Find the velocity at t=2.

3-5 Solving Equations with the Variable on Each Side Objectives SWBAT: 1) solve equations with the variable on each side 2) solve equations involving grouping.

What is Motion? Mechanics – The study of motion of objects Kinematics – The science of describing motion of objects.

3-3 Dividing Decimals Do Now Multiply   (-19.21)  (–2.1)

DRIVING RATIONALLY Antonia is driving from Oklahoma City to Dallas, a distance of 200 miles. After exactly 100 miles, she stops and determines that she.

2.1 Unit Rates Essential Question: When and why do I use proportional comparisons?

Essential Question: What are the different ways in which we can describe the velocity of a moving object? Science 7.

Slope and Direct Variation Today, you will need: A calculator Homework that is due today.

BIS 219 Week 2 Individual Club IT, Part One Check this A+ tutorial guideline at 219/BIS-219-Week-2-Individual-Club-IT-Part-

Describing Motion in One Dimension

Warmup A car that is bought for $24,000 is expected to lose all its value in 10 years a) Write an equation for straight line depreciation b) What is the.

Intro to Systems of Equations and Graphing

Calculating Speed A) John is walking down the hall. He travels 24 meters in 12 seconds. What is his average speed? ANSWER: 2 m/s.

Unit Rates and Proportional Reasoning

SLOPE = = = The SLOPE of a line is There are four types of slopes

with the following images?

A graphing calculator is required for some problems or parts of problems 2000.

Warm Up Graph each number on a number line. 1. – – –5 –4 –3 –2 –

Warm Up Graph each number on a number line. 1. – – –5 –4 –3 –2 –

Motion, Speed, Velocity and Acceleration

Chapter 2.2 Physical Science

GCSE Mathematics Targeting Grade C Unit 3 Algebra 3 Travel Graphs.

Presentation transcript:

Applications of Rates and Proportional Reasoning: Rate of Change Today you will learn to: Calculate the rate of change from a graph Calculate the slope of a line M7.A.2.2.1

Warm-up Problem: Unit Rates (Review) Four friends took a road trip to visit the Smithsonian in Washington D.C. They drove 520 miles in 5 hours. What was their average speed, in miles per hour? After their visit, they stopped at a sidewalk vender and bought 8 hotdogs for $4.00. What was the price per hot dog?

Rate of Change The rate of change is the speed at which a variable changes over a specific period of time. Graphically, the rate of change is represented by m, or the unit rate. To calculate the rate of change from a graph, determine how the change in y- values relates to the change in x-values. In the graph to the left, Ally graphed her allowance over six weeks. Based on her graph, you can see that her allowance is $10 per week.

Slope of a Line We sometimes refer to the rate of change as the SLOPE of a line. Essentially, it the is the unit rate ( m ), or y ÷ x. To determine the slope of a line, and, therefore, the rate of change, check out the following videos (2) from the Khan Academy. It is important to note that the rate of change does NOT have to be proportional, and can be negative. Graphical Slope of a Line Slope of a Line

Example: Rate of Change The science club is inflating a model of a hot air balloon, as shown in the graph below. At what rate is the diameter increasing?