Concept. Example 1 Find Rate of Change DRIVING TIME Use the table to find the rate of change. Explain the meaning of the rate of change.

Slides:



Advertisements
Similar presentations
WARM UP 1. Explain how to graph a linear equation written in slope-intercept form. 2. Explain how to graph a linear equation written in point-slope form.
Advertisements

3-3 Rate of change and Slope
slopeGraph lines Direct var par. & perp Function Relations
Lesson 7 MI/Vocab parallel lines perpendicular lines Write an equation of the line that passes through a given point, parallel to a given line. Write an.
SOLUTION EXAMPLE 1 A linear system with no solution Show that the linear system has no solution. 3x + 2y = 10 Equation 1 3x + 2y = 2 Equation 2 Graph the.
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.
Splash Screen. Then/Now I CAN use rate of change to solve problems and find the slope of a line. Note Card 3-3A Define Rate of Change and copy the Key.
Types of functions: Let's consider the following cell phone plans Unlimited minutes plan –$199 per month –No extra charge for minutes Pay by the minute.
EXAMPLE 4 Write an equation given two points
4-1A Rate of Change and the Slope of a Line Using a Graph
Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION.
SOLUTION EXAMPLE 4 Graph an equation in two variables Graph the equation y = – 2x – 1. STEP 1 Construct a table of values. x–2–1 012 y31 –3–5.
Ratios and Proportional Relationships
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).
3.3 Rate of Change and Slope
1.A 2.B 3.C 4.D 5Min /6 Honors Algebra Warm-up Write an equation in function notation for the following relationship. What is the rate? Time walking.
Daily Homework Quiz Review 5.3
Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.
6-1 Slope Objectives 1. find the slope of a line 2.use rate of change to solve problems.
Lesson 1 MI/Vocab rate of change slope Use rate of change to solve problems. Find the slope of a line.
Finding a Linear Model Section 2.4. Lehmann, Intermediate Algebra, 4ed Section 2.4 A company’s profit was $10 million in 2005 and has increased by $3.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary Key Concept: Rate of Change Example 1: Real-World Example:
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.
Algebra Concepts Chapter 3 Notes Note: We will only cover sections 3-1 and 3-3.
Welcome to Interactive Chalkboard Algebra 1 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION.
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.
Then/Now You found rates of change of linear functions. (Lesson 3–3) Write and graph direct variation equations. Solve problems involving direct variation.
ALGEBRA READINESS LESSON 8-5 Warm Up Lesson 8-5 Warm-Up.
FINDING THE SLOPE FROM 2 POINTS Day 91. Learning Target: Students can find the slope of a line from 2 given points.
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.
Divide. Warm-Up Exercises ANSWER 0 undefined ANSWER –1 1. – 7 – – 3 – – 5 – An Internet company had a profit of $2.6 million in.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary Key Concept: Rate of Change Example 1: Real-World Example:
A4.a How Do I Interpret Slope of a Line As A Rate Of Change? Course 3 Warm Up Warm Up Lesson Presentation Lesson Presentation.
The Slope of a Line 4.4 Objective 1 – Find the slope of a line using two of its points Objective 2 – Interpret slope as a rate of change in real-life situations.
To write another equivalent equation, multiply each side by x – 12y = 8 To write one equivalent equation, multiply each side by 2. SOLUTION Write.
Over Lesson 3–2 5-Minute Check 5 A.264 B.222 C.153 D.134 The equation P = 3000 – 22.5n represents the amount of profit P a catering company earns depending.
Rate of Change and Slope Lesson 3-3 Splash Screen.
HOMEWORK ANSWERS 4. Yes. The rate of change is constant 5. No. the rate of change is not constant.
§3-3 Rate of Change and Slope. Rate of Change Time Walking (seconds) Distance Walked (feet) This means you walked 4 feet every second.
Lesson 3-3 Menu In the figure, m 4 = Find m 2. 2.Find m 7. 3.Find m Find m Find m 11 + m 6. 6.In the figure, what is the measure of.
Objective: Use rate of change to solve problems. Find the slope of a line.
Rate of change and Slope Rise over Run The change of the rise over the change of the run.
1. The square root of 9 is 3 True
Splash Screen.
ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.
3.3 Rate of Change and Slope
Rate of Change and Slope
Splash Screen.
Five-Minute Check (over Lesson 3–2) Mathematical Practices Then/Now
3-3 Slope as Rate of Change
DIRECT VARIATIONS.
Concept.
Topic: Slopes of Lines Section: 3-3 Concept.
Using the Slope Formula
Solve a system of linear equation in two variables
Model Direct Variation
Model Direct Variation
Key Concept 1.
3-3 Slope as Rate of Change
Objective Find slope by using the slope formula..
Day 5 – Forms of Equation.
Splash Screen.
Slope or Rates of Change
Model Direct Variation
COURSE 3 LESSON 3-3 Understanding Slope
Section 7.1 Graphs, Slopes, Inequalities and Applications.
Splash Screen.
Students will be able to graph equations of lines.
Lesson 5-1 Warm-Up.
Presentation transcript:

Concept

Example 1 Find Rate of Change DRIVING TIME Use the table to find the rate of change. Explain the meaning of the rate of change.

Example 1 CELL PHONE The table shows how the cost changes with the number of minutes used. Use the table to find the rate of change. Explain the meaning of the rate of change.

Example 2 A Variable Rate of Change A. TRAVEL The graph to the right shows the number of U.S. passports issued in 2002, 2004, and Find the rates of change for 2002–2004 and 2004–2006. millions of passports years

Example 2 CYP A A. Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 1995–2000 and 2000–2005.

Example 3 A Constant Rate of Change A. Determine whether the function is linear. Explain.

Example 3 CYP A A. Determine whether the function is linear. Explain.

Concept

Example 4 A Positive, Negative, and Zero Slope A. Find the slope of the line that passes through (–3, 2) and (5, 5). Let (–3, 2) = (x 1, y 1 ) and (5, 5) = (x 2, y 2 ). Substitute. Answer: Simplify.

Example 4 CYP A A. Find the slope of the line that passes through (4, 5) and (7, 6).

Concept