The slope-intercept form of a line: y = mx + b. Graph the following family of lines using the graphing calculator: 1.y = 3x + 2 2.y = 5x + 2 3.y = -4.

Slides:

Advertisements

Similar presentations

Writing the Equation of a Line Using Slope-Intercept Form Chapter 5.1.

Advertisements

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.

 An equation of a line can be written in slope- intercept form y = mx + b where m is the slope and b is the y- intercept.  The y-intercept is where.

Find slope and y-intercept given an equation in standard form. 5.5 day 2 3x - 6y = 12.

Section 2.3 – Linear Functions and Slope-Intercept Form Consider a nonvertical line in the coordinate plane. If you move from any point on the line to.

3.5 Lines in the Coordinate Plane

2.5 Linear Equations. Graphing using table Graphing using slope and y-intercept (section 2.4) Graphing using x-intercept and y-intercept (section 2.5)

Finding the Intercepts of a Line

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)

Learn to use slopes and intercepts to graph linear equations.

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.

Objectives: Define and explain the components of the slope-intercept form of a linear equation. Use the slope-intercept form of a linear equation. Standards.

5.3 Slope-intercept form Identify slope and y-intercept of the graph & graph an equation in slope-intercept form. day 1.

Equations of Lines. Three forms of a line y = mx + bslope-intercept y-y 1 = m(x – x 1 )point-slope Ax + By = Cstandard form.

7.2 Linear Functions And Their Graphs

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Example 1 Identifying Slopes and y-intercepts Find the slope and y -intercept of the graph of the equation. ANSWER The line has a slope of 1 and a y -intercept.

Plot and label the ordered pairs in a coordinate plane. (Lesson 4.1) A(-5, 2), B(0, 5), C(-6, 0)

1 PRECALCULUS I Dr. Claude S. Moore Danville Community College Graphs and Lines Intercepts, symmetry, circles Slope, equations, parallel, perpendicular.

MTH 070 Elementary Algebra I

10.3 Slope-Intercept Form of Linear Equations CORD Math Mrs. Spitz Fall 2006.

Write an equation given the slope and y-intercept EXAMPLE 1 Write an equation of the line shown.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Linear Functions and Slope.

2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)

Sullivan Algebra and Trigonometry: Section 2.3 Objectives Calculate and Interpret the Slope of a Line Graph Lines Given a Point and the Slope Use the Point-Slope.

Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.2 Linear Functions and Their Graphs.

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.

8-3 & 8-4: Graphing Linear Functions Mr. Gallo. Graphing Linear Functions  Linear Function:  The graph of this function is a ____________ _______. 

2.3 – Slopes, Forms of Lines. Slope Slope = measure of steepness of a line in the Cartesian plane for two points Slope = m = Two ways to calculate slope:

Lesson 5.6 Point-Slope Form of the Equation of a Line.

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.

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

Writing Equations of a Line. Various Forms of an Equation of a Line. Slope-Intercept Form.

Section 2.5 Other Equations of Lines  Point-Slope Form (y – y 1 )=m(x – x 1 )  Special pairs of lines: Parallel Lines m 1 = m 2 Perpendicular lines m.

Algebra 2 Lesson 2-4 Writing Linear Equations. Different Forms of Linear Equations Slope-intercept Form: y = mx + b Standard Form: Ax + By = C Point-Slope.

2.4 Essential Questions What is the point-slope form?

Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:

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.

8.4 The Slope-Intercept Form of a Linear Equation Objective: To use the Slope-Intercept Form of a linear equation. Warm – up: Solve each equation for y.

X and Y Intercepts.

Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b (slope – intercept form)

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Linear Functions and Slope.

The Slope of a Line Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical.

2.3 Linear Functions and Slope-Intercept Form The slope of a nonvertical line is the ratio of the vertical change to the horizontal change between two.

Writing Linear Equations (Slope- Intercept Form).

5)Find the slope of the line passing through the two given points. a)(-3,5) and (-3,1) b)(4, 6) and (1,6)

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

EXAMPLE 1 Identify slope and y-intercept Identify the slope and y- intercept of the line with the given equation. y = 3x x + y = 22. SOLUTION The.

4.3 – Writing Equations in Point Slope Form. Ex. 1 Write the point-slope form of an equation for a line that passes through (-1,5) with slope -3.

6.4 Point-Slope Form and Writing Linear Equations Point-Slope Form of a Linear Equation –The point-slope form of the equation of a nonvertical line that.

Equations of Lines LF.2.AC.7: Write an equation given two points, a point and y-intercept, a point and slope.

When an equation is in slope-intercept form: Examples: Identify the slope of the line and the y- intercept for each equation. 1. y = 3x y = ½.

Slope-Intercept Form of a Linear Equation. Is this a linear equation? 3x + 2y = 6.

The y-intercept and slope-intercept form/ Writing linear equations from graphs. 1/11/15.

Linear Functions and Slope

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.

Jeopardy Inequalities Standard Form Slope, Y-Intercept, X-Intercept Systems of Equations Q $100 Q $200 Q $300 Q $400 Q $100 Q $200 Q $300 Q $400 Slope-

SOLVING LINEAR SYSTEMS by GRAPHING ADV133 Put in slope-intercept form: y = mx + b. y = 4x – 1 y = –x + 4 The solution to a system of linear equations is.

2.4 More about Linear Equations

Introduction to Linear Functions 3.1/3.2 And Properties of Linear Function Graphs.

2.6 Finding equations of lines. Review Slope-Intercept Form: y = mx + b Point-Slope Form: y – y 1 = m (x – x 1 )

Standard Form Equation of a Line Name Feb 29, 2011 Are these equations of the SAME LINE? y = x + 2 x – y = -2.

5.3 Slope-intercept form Identify slope and y-intercept of the graph & graph an equation in slope- intercept form. day 2.

Write the Equation of the Line You will need to take notes on GRAPH paper today. Copy the graph below and we will use it to answer multiple questions.

Writing Linear Equations in Slope Intercept Form Goals: Write linear equations given 2 points. Decide which form of a line to use given initial information.

The slope-intercept form of a line: y = mx + b

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.

y = mx + b y – y1 = m (x – x1) Topic: Writing Equations given two

Presentation transcript:

The slope-intercept form of a line: y = mx + b

Graph the following family of lines using the graphing calculator: 1.y = 3x y = 5x y = -4 x y = 1/2 x + 2 All of these equations are written in y = mx+b form. What does m represent in each equation? Check your hypothesis by using the table feature of the calculator.

Graph the following family of lines using the graphing calculator: 1.y = 3x y = 3x y = 3x 4.y = 3 x + 8 All of these equations are written in y = mx+b form. What does b represent in each equation? Check your hypothesis by using the table feature of the calculator.

Given y = mx + b  m represents the slope of the line  b represents the y-intercept -- the point where the line intercepts or crosses the y-axis.

Graphing lines in the form y = mx + b is very easy since you know one point, the y-intercept, and the slope. Graph each of the following: 1.y = 2x y = - x – 3 3.y = 4x 4.y = - 2

Finding the equations of lines is very easy if you know the y-intercept and slope. Find the equation of the line: 1.t hat passes through the origin with slope – 2. 2.w ith y–intercept of 4 and slope 2/3. 3.t hat is horizontal and passes through the point ( 2, 5)

What if the equation is not given in y = mx + b form? Graph the equation whose standard form is 3x + 2y = 6.  Strategy 1: Rewrite the equation in y = mx + b form.  Strategy 2: Find the x-intercept and the y- intercept.

To find the x-intercept and the y-intercept of a line written in standard form:  Let x = 0 to find the y-intercept.  Let y = 0 to find the x-intercept.  Example: Find the x-intercept and the y- intercept of the line 3x – 5y = 15. Then graph the line.

Graphing equations in different forms:  Point-slope form: y – y 1 = m(x – x 1 ) Use a point (x 1, y 1 ) and the slope, m.  Standard form Ax + By = C  Rewrite in y = mx + b form OR  Find the x-intercept and the y-intercept OR  Make a table of solutions.  Slope-intercept form y = mx + b Use the y-intercept and the slope.

Assignment:  6.4 #19-45 odds Due Wednesday 1/14/04  6.5 #13-25 all. Use graph paper. Write the equation next to each graph. Due Thursday 1/15/05