Algebra 2 Chapter 2.2 Linear Relations & Functions Target Goals: 1.Identify linear relations and functions 2.Determine the intercepts of linear equations/functions.

Slides:

Advertisements

Similar presentations

Gold Day – 2/18/2015 Blue Day – 2/19/2015

Advertisements

2.2 – Linear Equations and their Intercepts. Recall… Linear Equation = equation in the form: ax + by = c – Highest Power (Degree) = 1 Non-Linear Equation.

F(x ). Names Linear Constant Identity Quadratic Cubic Exponential And many more! Straight Line Horizontal Line Slanted Line Parabola Half Parabola Twisted.

Warm Up 0?1? 2? Graph the linear functions.0?1? 2?

Notes Over 4.3 Finding Intercepts Find the x-intercept of the graph of the equation. x-intercept y-intercept The x value when y is equal to 0. Place where.

4.5 Graphing Linear Equations

Slope – Intercept Form What do all the points on the y-axis have in common? What do all the points on the x-axis have in common?

Finding the Intercepts of a Line

Slope-Intercept Form Page 22 10/15. Vocabulary y-Intercept: the point at which a function crosses the y-axis (0, y) x-intercept: the point at which a.

Graphs of Equations Finding intercepts of a graph Graphically and Algebraically.

2.2 Graphs of Equations in Two Variables Chapter 2 Section 2: Graphs of Equations in Two Variables In this section, we will… Determine if a given ordered.

3.2 Intercepts. Intercepts X-intercept is the x- coordinate of a point when the graph cuts the x-axis Y-intercept is the y- coordinate of a point when.

Standard Form & x-intercepts & y-intercepts

Objectives The student will be able to:

We will identify linear equations and functions.

Graphing Using x & y Intercepts

Algebra II w/ trig.  Coordinate Plane  Ordered pair: (x, y)  Relation: a set of ordered pairs(mapping, ordered pairs, table, or graphing)  Domain:

Submitted to - Sh.Bharat Bhushan Sir Submitted by- Mayank Devnani

Section 4.5: Graphing Linear Equations Objectives The student will be able to: EA graph linear functions. 2. write equations in standard form.

Bellwork. Objective 1 The student will be able to: graph ordered pairs on a coordinate plane.

Slide 1 © 2004 By Default! A Free sample background from Graphing Linear Equations Objective: Students will determine whether.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3.

Warm Up #10 1.) Graph 5x + 7y =35 2.) Graph y= 2x -3.

Graph the following Y = 4 X = 3 Y = -5x + 2 6x + 3y = 9.

2.2 – Linear Equations. Linear equation 2.2 – Linear Equations Linear equation – equation with only addition,

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–1) CCSS Then/Now New Vocabulary Example 1:Identify Linear Functions Example 2:Real-World Example:

Relations and Functions

Graphing Equations of Lines Using x- and y-Intercepts.

Section 2.2 Notes: Linear Relations and Functions.

Chapter 2 Section 2. State whether is a linear function. Explain. Answer: This is a linear function because it is in the form.

Unit 1 – First-Degree Equations and Inequalities

Chapter 2 Examples Section 2 Linear Functions. Objective: Students will identify patterns with linear forms of equations and functions. They will also.

Holt Algebra Identifying Linear Functions Warm Up 1. Solve 2x – 3y = 12 for y. 2. Graph for D: {–10, –5, 0, 5, 10}.

Graphing Linear Functions 1. graph linear functions. 2. write equations in standard form.

Chapter 2 Linear Relations and Functions BY: FRANKLIN KILBURN HONORS ALGEBRA 2.

2.2 Linear Relations and Functions. A. 27 B. 64 C. 9 D. 10.

Activity 1.6 Depreciation. In your groups… Read page 51 Complete exercises 1 and 2 in your groups Don’t forget –Average rate of change is –UNITS!!!!!!!!!!!!!!!!!!!!!!!!!

Over Lesson 2–1 5-Minute Check 1 Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.

College Algebra Acosta/Karwoski. CHAPTER 1 linear equations/functions.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–1) Then/Now New Vocabulary Example 1:Identify Linear Functions Example 2:Real-World Example:

CHAPTER 3 GRAPHING LINEAR FUNCTIONS  What you will learn:  Determine whether relations are functions  Find the domain and range of a functions  Identify.

Drill #17 Find the value of the following if f(x) = 1. f( 2 ) 2. f( ½ ) 3.f(-1) 4.f(3a)

September 17, Objectives Students will be able to: Identify linear equations and functions, Write linear equations in standard form and graph them.

TLW identify linear equations and intercepts.

Splash Screen. CCSS Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables.

Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION.

2-2 Linear Equations Obj: identify linear equations/functions Write linear equations in standard form.

Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.

Linear Expressions Chapter 3. What do you know about Linear Relations?

Holt Algebra Using Intercepts Warm Up 1. 5x + 0 = –10 Solve each equation. – – = 0 + 3y x + 14 = –3x –5y – 1 = 7y + 5.

Bell Ringer Rewrite from standard to slope intercept form: 1. 2x + 4y = x + 8y = 32 Learning Target: I can graph the equation of a line from the.

Drill #18 a.) Graph the following relation (use an x-y chart). b.) state the domain and the range, c.) identify if it one-to-one, onto, both or neither.

Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:

Equations with fractions can be simplified by multiplying both sides by a common denominator. 3x + 4 = 2x + 8 3x = 2x + 4 x = 4 Example: Solve

Equations in two variables can be represented by a graph. Each ordered pair (x,y) that makes the equation true is a point on the graph. Graph equation.

7.3 Linear Equations and Their Graphs Objective: To graph linear equations using the x and y intercepts To graph horizontal and vertical lines.

Graphing Linear Equations Chapter 7.2. Graphing an equation using 3 points 1. Make a table for x and y to find 3 ordered pairs. 2. I choose 3 integers.

Lesson 5-4: Graphing Linear Equations

Integrated Mathematics. Objectives The student will be able to:: 1. graph linear equations. 2. write equations in point- slope form.

Bellwork Read the Why? On pg. 69 of your text book. Answer the following questions 1.) What does the value of x mean for this situation? 2.) What does.

Aim: How can we identify linear functions and write linear equations

Graphing Graph of a Linear Equation x and y Intercepts Slope of a Line

Relations, Functions, and Linear Equations

Warm Up – August 15, Does y vary directly with x? If so, what is the constant of variation and the function rule? 2. Determine whether y varies.

The relation between the fuel economy and speed of a given car was recorded. What is the fuel economy at 20mph? Problem of the Day f(20) = 15 c)

Chapter 2 Section 2 Linear Equations.

Sec 6-3-b Learning Objectives The student will be able to:

Presentation transcript:

Algebra 2 Chapter 2.2 Linear Relations & Functions Target Goals: 1.Identify linear relations and functions 2.Determine the intercepts of linear equations/functions 3.Graph linear equations/functions using intercepts

New Vocabulary Linear Relations – Relations with straight lines when graphed Linear Equation – Has no operations except addition, subtraction, & multiplication of a variable by a constant – Fractions of numbers are ok, but variable can NOT be in the denominator! – No exponents on variables other than 1 (which usually is not written)

Linear vs. Non-Linear Linear EquationsNon-Linear Equations

Function Notation vs. Equations f(x) = y f(x) replaces the dependent variable (y) y = 2x + 1  f(x) = 2x + 1

Characteristics of Linear Functions Graph is a straight line Only operations seen are +, -, or multiplication of variable and a constant (a number) No variables in the denominator Exponents on variables are only 1 No variables are multiplied together

Practice: State whether each function is a linear function. Write yes or no and explain your answer. Yes!! No – variable in the denominator No – exponent on variable is not 1

Connection to Order of Operations/Formulas/Real-Life! Ex 4) The linear function can be used to find the number of degrees Fahrenheit f (C) that are equivalent to a given number of degrees Celsius C. On the Celsius scale, normal body temperature is 37°C. What is it in degrees Fahrenheit?

INTERCEPTS y-intercept: the point where the line crosses the y-axis; (0, b) x-intercept: the point where the line crosses the x-axis; (a, 0)

Practice: Find the x-intercept and the y- intercept of the graph of the linear equation. Then graph the equation. Ex 5) 2x + 5y – 10 = 0 x-intercept 2x + 5y – 10 = 0 2x + 5(0) – 10 = 0 2x – 10 = 0 2x = 10 x = 5 (5, 0) y-intercept 2x + 5y – 10 = 0 2(0) + 5y – 10 = 0 5y – 10 = 0 5y = 10 y = 2 (0, 2)

Practice: Find the x-intercept and the y- intercept of the graph of the linear equation. Then graph the equation. Ex 6) -2x + y – 4 = 0 x-intercept -2x + y – 4 = 0 -2x + (0) – 4 = 0 -2x – 4 = 0 -2x = 4 x = -2 (-2, 0) y-intercept -2x + y – 4 = 0 -2(0) + y – 4 = 0 y – 4 = 0 y = 4 (0, 4)