4.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Find Slope and Rate of Change.

Slides:



Advertisements
Similar presentations
Objective - To find the slope of a line.
Advertisements

Do Now 10/29/09 Copy HW in your planner.  Text page 239, #4-32 even In your notebook, answer the following question. There are two skateboard ramps at.
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.
EXAMPLE 2 Find a negative slope Find the slope of the line shown. m = y 2 – y 1 x 2 – x 1 Let (x 1, y 1 ) = (3, 5) and (x 2, y 2 ) = (6, –1). –1 – 5 6.
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.
TODAY IN ALGEBRA…  Warm Up: Find the x and y intercepts and graph  Learning Goal: 4.4 You will find the slope of a line and interpret as a rate of change.
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.
Slope and Rate of Change Lesson 2.3 Warm-up Divide: 0 Undefined An Internet company had a profit of $2.6 million in retail sales over the last five years.
EXAMPLE 6 Use a graph to find and compare rates of change COMMUNITY THEATER A community theater performed a play each Saturday evening for 10 consecutive.
Warm Up Add or subtract (–6)2. – –7 – – (–1) –2 – Find the x- and y-intercepts of 2x – 5y = 20. x-int.: 10; y-int.: –4.
Fit a Line to Data Warm Up Lesson Presentation Lesson Quiz.
4-1A Rate of Change and the Slope of a Line Using a Graph
10.8 Warm Up Warm Up Lesson Presentation Lesson Presentation Compare Linear, Exponential, and Quadratic Models.
Rate of Change and Slope
Slope = change in y change in x Understanding Slope COURSE 3 LESSON 3-3 Using coordinates, find the slope of the line between P (–2, 3) and Q (–1, –1).
Bell Quiz. Objectives Find the slope of a line using the slope formula.
4.4 Find Slope and Rate of Change
Unit 1. Warm-Up – X.X Vocabulary – X.X Holder Holder 2 Holder 3 Holder 4.
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
4-3 rate of change and slope
Lesson 1 MI/Vocab rate of change slope Use rate of change to solve problems. Find the slope of a line.
3.6 Model Direct Variation
Then/Now You graphed ordered pairs in the coordinate plane. (Lesson 1–6) Use rate of change to solve problems. Find the slope of a line.
5.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Linear Equations in Point-Slope Form.
Holt McDougal Algebra Rate of Change and Slope 4-3 Rate of Change and Slope Holt Algebra 1 Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation.
Holt McDougal Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.
Warm Up Evaluate and simplify the ratios when x = 2 and y = –2. ANSWER 1. x 5 – y – 3 4 – x y – – 3. A cross-country skier traveled 14 miles.
4.4 Finding Slope and Rate of Change. How Would You Describe Slope?
EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute.
Unit 1 – Chapters 1 and 4.
ALGEBRA READINESS LESSON 6-4 Warm Up Lesson 6-4 Warm-Up.
Divide. Warm-Up Exercises ANSWER 0 undefined ANSWER –1 1. – 7 – – 3 – – 5 – An Internet company had a profit of $2.6 million in.
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Holt Geometry 3-5 Slopes of Lines 3-5 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
First, Let’s Warm Up Evaluate each equation for x = –1, 0, and y = 3x 2. y = x – 7 3. y = 2x y = 6x – 2 –3, 0, 3 –8, –7, –6 3, 5, 7 –8, –2,
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Holt Geometry 3-4 Slopes of Lines 3-4 Slopes of Lines Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Find the x and y intercepts: y = 7x – 3 -4y + x = 8 2x – 5y = 20
Evaluate and simplify the ratios when and. x2 = For use with pages xxx–xxx Daily Warm-Up Exercises For use with pages 281–289 y = 2 – 1. 5 – x 3 + y 2.
INTRO TO DISTANCE, DISPLACEMENT, SPEED, VELOCITY QUIZ REVIEW.
Warm up 1.Find the solutions. 2.Find the interval of decrease. (-1, 0) (5, 0) x > 2.
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.
Pg #3, 4-24eoe, 36-39, 46, Quiz 1 Pg. 232 #4-12e, 13.
2.2 Constant Rates of Change
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Warm-Up Exercises Lesson x – 2y = –8 2. –9x + 3y = 21 ANSWER y = 2x + 4 Rewrite the equation so y is a function of x. y = 3x + 7.
Slope of a Line 11-2 Warm Up Problem of the Day Lesson Presentation
Warm Up Find the value of m
Preview Warm Up California Standards Lesson Presentation.
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Warm Up Find the value of m undefined.
Concept.
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Rate of Change and Slope
1.4 Types of Functions and Their Rates of Change
4.4 Find Slope and Rate of Change
Rate of Change and Slope
8 3 . Slope You can use ratios to describe the slope of a line.
Rate of Change and Slope
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Graph Each Equation Using the Intercepts
3-6 Warm Up Find the value of m
COURSE 3 LESSON 3-3 Understanding Slope
Lesson 5-1 Warm-Up.
Presentation transcript:

4.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Find Slope and Rate of Change

4.4 Warm-Up Evaluate and simplify the ratios when x = 2 and y = –2. ANSWER 1. x 5 – y – 3 4 – x y – –

4.4 Warm-Up 3. A cross-country skier traveled 14 miles in 3.5 hours. Use the formula d = rt where d is distance, r is rate, and t is time, to find the average rate of speed. ANSWER 4 mi/h

4.4 Example 1 Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = = Simplify. Substitute. Write formula for slope. Find the slope of the line shown.

4.4 Guided Practice Find the slope of the line that passes through the points. ANSWER 3 1. (5, 2) and (4, –1) 2. (–2, 3) and (4, 6) 1 2 ANSWER 3. (, 5) and (, –3) ANSWER 2

4.4 Example 2 Find the slope of the line shown. m = y 2 – y 1 x 2 – x 1 Let (x 1, y 1 ) = (3, 5) and (x 2, y 2 ) = (6, –1). –1 – 5 6 – 3 = – 6 3 = = –2–2 Write formula for slope. Substitute. Simplify.

4.4 Example 3 Find the slope of the line shown. Let (x 1, y 1 ) = (–2, 4) and (x 2, y 2 ) = (4, 4). m = y 2 – y 1 x 2 – x 1 4 – 4 4 – (–2) = 0 6 = = 0 Write formula for slope. Substitute. Simplify.

4.4 Example 4 Find the slope of the line shown. Let (x 1, y 1 ) = (3, 5) and (x 2, y 2 ) = (3, 1). m = y 2 – y 1 x 2 – x 1 Write formula for slope. 1 – 5 3 – 3 = Substitute. Division by zero is undefined. ANSWER Because division by zero is undefined, the slope of a vertical line is undefined. – 4 0 =

4.4 Guided Practice Find the slope of the line that passes through the points. 4. (5, 2) and (5, –2) ANSWERundefined 5. (0, 4) and (–3, 4) 0 ANSWER 6. (0, 6) and (5, –4) ANSWER –2–2

4.4 Example 5 INTERNET CAFE The table shows the cost of using a computer at an Internet cafe for a given amount of time. Find the rate of change in cost with respect to time.

4.4 Example 5 Rate of change = change in cost change in time 14 – 7 4 – 2 = 7 2 = 3.5 = ANSWER The rate of change in cost is $3.50 per hour. SOLUTION

4.4 Guided Practice The table shows the distance a person walks for exercise. Find the rate of change in distance with respect to time. 7. EXERCISE ANSWER 0.05 mi / min

4.4 Example 6 COMMUNITY THEATER A community theater performed a play each Saturday evening for 10 consecutive weeks. The graph shows the attendance for the performances in weeks 1, 4, 6, and 10. Describe the rates of change in attendance with respect to time.

4.4 Example 6 SOLUTION Find the rates of change using the slope formula. Weeks 1–4: 232 – – 1 = = 36 people per week Weeks 4–6: 204 – – 4 = –28 2 = –14 people per week Weeks 6–10: 72 – – 6 = –132 4 = –33 people per week ANSWER Attendance increased during the early weeks of performing the play. Then attendance decreased, slowly at first, then more rapidly.

4.4 Guided Practice WHAT IF? How would the answer to Example 6 change if you knew that attendance was 70 people in week 12? 8. Sample answer: The attendance did not decrease as rapidly between weeks 10 and 12. ANSWER

4.4 Example 7 COMMUTING TO SCHOOL A student commutes from home to school by walking and by riding a bus. Describe the student’s commute in words.

4.4 Example 7 The first segment of the graph is not very steep, so the student is not traveling very far with respect to time. The student must be walking. The second segment has a zero slope, so the student must not be moving. He or she is waiting for the bus. The last segment is steep, so the student is traveling far with respect to time. The student must be riding the bus. SOLUTION

4.4 Guided Practice WHAT IF? Using the graph in Example 7, draw a graph that represents the student’s commute from school to home. 9. ANSWER

4.4 Lesson Quiz Find the slope of the line that passes through the points 1. (12, –1) and ( –3, –1) ANSWER 0 2. (–2, 6) and (4, –3) ANSWER 3 2 –

4.4 Lesson Quiz 3. The graph shows the ticket sales for a school dance on day 1, day 3, day 6, and day 9 of ticket sales. Describe the rates of change in ticket sales with respect to time. ANSWER Ticket sales grew moderately, declined slightly, and then had another moderate rate of increase.