Remember: Slope is also expressed as rise/run. Slope Intercept Form Use this form when you know the slope and the y- intercept (where the line crosses.

Slides:

Advertisements

Similar presentations

§ 2.4 The Slope of a Line.

Advertisements

Parallel & Perpendicular Lines

Writing and Graphing Linear Equations

Linear Equations Ax + By = C.

Copyright © Cengage Learning. All rights reserved.

Writing and Graphing Equations of Lines

4.1 Introduction to Linear Equations in Two Variables

7-1 Slope Objectives: Find the slope of a line given the coordinates of two points on the line.

Objectives Use slope-intercept form and point-slope form to write linear functions. Write linear functions to solve problems. Recall from Lesson 2-3 that.

Slope-Intercept and Point-Slope Forms of a Linear Equation

Do Now Find the slope of the line passing through the given points. 1)( 3, – 2) and (4, 5) 2)(2, – 7) and (– 1, 4)

Bell Work Solve for “y” 1.) 3x – 2y = -8 2.) 5x – y + 12 = 3x ) 3x – 4y = -7y – 12.

7.2 Review of Equations of Lines; Linear Models

Writing linear equations in slope-intercept form

Slope and Linear Equations

Objectives Determine whether a function is linear.

Gold Day – 2/24/2015 Blue Day – 2/25/2015.  Unit 5 – Linear functions and Applications  Review – slope, slope intercept form  Standard Form  Finding.

Learning Objectives for Section 1.2 Graphs and Lines

Solving Linear Equations with One Variable

Writing Linear Functions

1.2 Linear Equations in Two Variables

LINEAR EQUATIONS PART I

Solving Equations. Is a statement that two algebraic expressions are equal. EXAMPLES 3x – 5 = 7, x 2 – x – 6 = 0, and 4x = 4 To solve a equation in x.

Linear Systems of Equations

6-1 System of Equations (Graphing): Step 1: both equations MUST be in slope intercept form before you can graph the lines Equation #1: y = m(x) + b Equation.

Slope and Rate of Change

Copyright © Cengage Learning. All rights reserved. 1.1 Lines in the Plane.

Graphing Linear Equations. Linear Equation An equation for which the graph is a line.

Section 6-2 Slope-Intercept Form. How to Graph a Linear Equation It must be in the slope – intercept form. Which is: y = mx + b slope y-intercept.

2.5 Writing Equation of a Line Sept 19, Equations of a Line equation written in the form Ax + By = C where A and B are not both zero Slope-Intercept.

Slope-Intercept Form of an Equation © 2002 by Shawna Haider.

Equations of Lines and Graphing Them Equations of Lines Vertical line x = # Horizontal line y = # Slope, y-intercept y=mx+b Standard Form Ax+By = C using.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 3 Equations and Inequalities in Two Variables; Functions.

5-3 Slope Intercept Form A y-intercept of a graph is the y-coordinate of a point where the graph crosses the y-axis. *Use can use the slope and y-intercept.

Welcome to MM 212 Unit 4 Seminar!. Graphing and Functions.

Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.

1.Given slope (m) and y-intercept (b) create the equation in slope- intercept form. 2. Look at a graph and write an equation of a line in slope- intercept.

C ollege A lgebra Linear and Quadratic Functions (Chapter2) 1.

Advanced Algebra 1. Slope-Intercept Form Point-Slope Form.

§ 2.5 Equations of Lines. Martin-Gay, Intermediate Algebra: A Graphing Approach, 4ed 22 Slope-Intercept Form of a line y = mx + b has a slope of m and.

Slope of a Line Chapter 7.3. Slope of a Line m = y 2 – y 1 x 2 – x 1 m = rise run m = change in y change in x Given two points (x 1, y 1 ) and (x 2, y.

Warm-up Presentation Lesson Quiz

Graphing Linear Equations

Linear Equations in Two Variables

Ex 1: Write the equation of the graphed line in slope-intercept form.

LEARNING TARGETS: 1. TO IDENTIFY SLOPE FROM A TABLE OF VALUES. 2. TO IDENTIFY SLOPE FROM A GRAPH. 3. TO IDENTIFY SLOPE FROM 2 POINTS. 4. TO IDENTIFY SLOPE.

1.2 Slopes and Intercepts Objectives: Graph a linear equation. Write a linear equation for a given line in the coordinate plane. Standards: K Apply.

Copyright © 2011 Pearson Education, Inc. Linear Equations in Two Variables Section 1.4 Equations, Inequalities, and Modeling.

Warm Up 1. 4x + 2y = x + 2 = 6y Solve each equation for y. y = –2x Find the slope of the line that contains (5, 3) and (–1, 4). 4. Find the.

Writing and Graphing Linear Equations

Rate of Change and Slope Objectives: Use the rate of change to solve problems. Find the slope of a line.

Writing and Graphing Linear Equations Linear equations can be used to represent relationships.

Point-Slope Form The line with slope m passing through the point (x1, y1) has an equation the point –slope form of the equation of a line.

Understand linear equations and its types. Form the linear equations involving slopes of different situations. Students and Teachers will be able to.

WARM-UP Solve each equation for y 1) 2) Determine if the following points are on the line of the equation. Justify your answer. 3) (3, -1) 4) (0, 1)

Point Slope Form To write an equation with the slope and a point that is not the y intercept.

GRE: Graphical Representations

Lesson 3-4: Graphs of Linear Equations Objective: Students will: recognize linear equations graph linear equations graph horizontal and vertical lines.

THE EQUATION OF A LINE By: Mr. F. A. Ogrimen Jr..

7-3 Writing equations in Slope- Intercept form Objectives: Write a linear equation in Slope-intercept form given the slope and y intercept.

Holt McDougal Algebra Slope-Intercept Form Warm Up Find each y-intercept. 1. y = 3x x – 3y = 12 Find each slope x + 2y = x.

Slopes of Parallel and Perpendicular Lines. Different Forms of a Linear Equation  Standard Form  Slope-Intercept Form  Point-Slope Form  Standard.

1 Review Linear relationships. 2 Let’s investigate the relationship between x and y denoted by y = -2x – 2. We’ll complete the table and graph it. xy.

Warm Up If f(x)= 3x 2 + 2x, find f(3) and f(-2). Check Yourself! If g(x)= 4x 2 – 8x + 2 find g(-3)

Chapter 2 Functions and Linear Equations. Functions vs. Relations A "relation" is just a relationship between sets of information. A “function” is a well-behaved.

Point-Slope Form Linear Equations in Two Variables.

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

Linear Equations & Functions

Writing Linear Equations Given Two Points

Presentation transcript:

Remember: Slope is also expressed as rise/run.

Slope Intercept Form Use this form when you know the slope and the y- intercept (where the line crosses the y-axis). y = mx + b m = slope b = y-intercept (where line crosses the y-axis.)

Horizontal LinesVertical Lines y = 3 (or any number) Lines that are horizontal have a slope of zero. Horizontal lines have "run", but no "rise". The rise/run formula for slope always yields zero since the rise = 0. Since the slope is zero, we have y = mx + b y = 0x + 3 y = 3 This equation also describes what is happening to the y-coordinates on the line. In this case the y-coordinates are always 3. x = -2 (or any number) Lines that are vertical have no slope (it does not exist). Vertical lines have "rise", but no "run". The rise/run formula for slope always has a zero denominator and is undefined. The equations for these lines describe what is happening to the x-coordinates. In this example, the x-coordinates are always equal to -2.

Examples using Slope-Intercept Form: 1. Find the slope and y-intercept for the equation 2y = -6x + 8. First solve for "y =": y = -3x + 4 Remember the form: y = mx + b Answer: the slope (m) is -3 the y-intercept (b) is 4 2. Find the equation of the line whose slope is 4 and the coordinates of the y-intercept are (0,2). In this problem m = 4 and b = 2. Remember the form: y = mx + b and that b is where the line crosses the y-axis. Substitute: y = 4x + 2

» Another commonly used form is the of the equation of a line. » Standard (or general) form: Ax + By = C » In this form, notice that the variable terms are on the left side of the equation and » the constant term is on the right. A, B, and C represent real numbers and A and B » are not both zero.

».». Write original equation Multiply each side by 5. 5y= 2x - 15Use distributive property. -2x + 5y = -15Subtract 2x from each side.

» A linear equation can have more than one standard form. For instance, if you » multiply each side of the standard form above by -1, you get 2x - 5y = 15, » which is also in standard form.

» Write the standard form of an equation of the line passing through (-4, 3) with » a slope of -2. » SOLUTION » You are given a point on the line and its slope, so you can write the point-slope » form of the equation of the line.

Write point-slope form. y - 3 = -2[x - (-4)] y - 3 = -2(x + 4)Simplify. y - 3 = -2x - 8Use distributive property. 2x + y = -5Add 2x and 3 to each side.