Lesson 13 Graphing linear equations. Graphing equations in 2 variables 1) Construct a table of values. Choose a reasonable value for x and solve the.

Slides:

Advertisements

Similar presentations

Ch. 6.1: Solve Quadratic Equations by Graphing

Advertisements

Solving Quadratic Equations – Graphing Method

Graphing Linear Functions

2.4 Graphing Linear Equation Sept 4, Y-intercept a point where a graph intersects the y-axis Vocabulary equation written in the form Ax + By = C.

WARM UP Evaluate the expression – – ÷ – ÷ – 8 ÷ Minutes Remain.

Lines with Zero Slope and Undefined Slope

~ Chapter 6 ~ Algebra I Algebra I Solving Equations

Quick graphs using Intercepts 4.3 Objective 1 – Find the intercepts of the graph of a linear equation Objective 2 – Use intercepts to make a quick graph.

Linear Equations in Two Variables

To solve equations using Intersect method with a graphing calculator Process 1.Enter y 1 = (left side of the equation). ENTER 2.Enter y 2 = (right side.

Solving Systems of Equations. Graphing There are three methods to solving systems of equations by graphing: 1)Write both equations in slope – intercept.

4.1 Introduction to Linear Equations in Two Variables

Rectangular Coordinate System

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

Introduction Many relationships can be represented by linear equations. Linear equations in two variables can be written in the form y = mx + b, where.

X y 1 st Quadrant2 nd Quadrant 3 rd Quadrant4 th Quadrant 13.1 – The Rectangular Coordinate System origin x-axis y-axis.

Objectives Determine whether a function is linear.

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.

Creating and Graphing Linear Equations in Two Variables ~Adapted from Walch Education.

Back to last slideMain Menu Graphing, Max/Min, and Solving By Mrs. Sexton Calculator Tips.

Introduction We have studied the key features of the graph of a parabola, such as the vertex and x-intercepts. In this lesson, we will review the definitions.

Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola.

5.1 Graphing Quadratic Functions Do now: Make up three examples of linear functions. How do you know they are linear? OBJ: to graph quadratic functions.

Objectives: 1. To identify quadratic functions and graphs 2. To model data with quadratic functions.

Graphing Quadratic Equations. What does a quadratic equation look like? One variable is squared No higher powers Standard Form y = ax 2 + bx + c y = x.

Chapter 4 Section 4-1 Solving Quadratic Equations in Calculator.

3.2 Graphing Functions and Relations

SOLVING & GRAPHING LINEAR EQUATIONS

Graphing Linear Equations

What is the slope of a line parallel to the line seen below? m= -1/3

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

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

Holt Algebra Graphing Linear Functions Meteorologists begin tracking a hurricane's distance from land when it is 350 miles off the coast of Florida.

Holt Algebra Graphing Linear Functions 2-3 Graphing Linear Functions Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation.

Journal Entry Equation of a Line May 1, Slope Slope is a measure of the steepness of a line. Slope is calculated as. Remember rise is the vertical.

1 Learning Objectives for Section 1.2 Graphs and Lines The student will be able to identify and work with the Cartesian coordinate system. The student.

Coordinates and Graphs in the Plane. Coordinate Plane x-axis y-axis origin.

Unit 4 Seminar GRAPHS 4.1 Variation 4.2 Linear Inequalities

2.4 Graphing Linear Equation Sept 12, Y-intercept a point where a graph intersects the y-axis Vocabulary equation written in the form Ax + By =

Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial.

Equation of a line.

Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.

MTH 091 Section 13.3 Graphing with x- and y-intercepts Section 13.4 Slope.

TI-83 An Introduction to Graphing Mathematics Staff Development Lincoln Public Schools August 25, 2005 © Jerel L. Welker

Today in Algebra 2 Go over homework Need a graphing calculator. More on Graphing Quadratic Equations Homework.

Figure 1.1a Evaluating Expressions To evaluate an algebraic expression, we may substitute the values for the variables and evaluate the numeric expression.

Y = x 2 – 4x – 5 xy Vertex? Max or Min? Axis of Symmetry? Do Now 1)

Graphing Linear Equations

Solving Absolute Value Equations The absolute value of x is defined as Example 1.

Chapter 3 Section 1 Copyright © 2011 Pearson Education, Inc.

Lesson Seven: Key Features of Linear and Quadratic Relationships

0.3 Linear Inequalities Aug 29, Graphing x = # Ex. Graph x = -3 The x coordinate is -3 no matter what the value of y is. xy Choose any.

Pre-Algebra 11-2 Slope of a Line 11-2 Slope of a Line Pre-Algebra Homework & Learning Goal Homework & Learning Goal Lesson Presentation Lesson Presentation.

Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach.

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

Finding x-intercepts, Solving Equations and Solving Inequalities by Graphing.

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.

Solving Systems By Graphing. Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept form for the equation of a line Slope = rise run.

Chapter-4(part 1) Graphing Linear Equations and Functions By: Donna, Fannie, Ashley and Nick.

Graphing Lines Using Slope Intercept Form Algebra 1 Glencoe McGraw-HillLinda Stamper.

Table of Values Using Auto Mode Set the calculator to automatically generate a table of values for y given that x Figure 3.1a Set up the table. Set a minimum.

Lesson 27 Connecting the parabola with the quadratic function.

Quick Graphs of Linear Equations

Equations of Lines in the Coordinate Plane

* Graphing * Max/Min * solving

Warm up Put each of the following in slope intercept form 6x + 3y = 12

Solving systems of equations by graphing

Graphing linear equations

Presentation transcript:

Lesson 13 Graphing linear equations

Graphing equations in 2 variables 1) Construct a table of values. Choose a reasonable value for x and solve the equation for y. Repeat this step 3 times.1) Construct a table of values. Choose a reasonable value for x and solve the equation for y. Repeat this step 3 times 2) Plot the points represented by the solutions to the equation 3) Connect the points to form a line. extend the line and draw arrows on the ends to indicate the line extends to infinity.

Graphing using intercepts The points where the graph intersects the axes on the coordinate plane are called the intercepts. The point where the graph intersects the x-axis is called the x- intercept. The point where the graph intercepts the y-axis is called the y-intercept.

Graphing using intercepts To find the x-intercept, let y = o, solve the equation for x. To find the y-intercept, let x=0, solve the equation for y Plot and connect the intercepts. Extend the line and add arrows to the ends

Slope of a line The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run). m = y 2 -y 1 = rise x 2 -x 1 run

Slope intercept form of a linear equation A linear equation written in the form y=m x +b is written in slope - intercept form, where m is the slope of the line, and b is the y- intercept

Moving from point to point using the slope Positive slope up or down right left Negative slope up or down left right

practice 1) Graph the equation y=-1/2 x + 3 A) by constructing a table of values B) using the intercepts C) using the slope and y-intercept 2) graph -x +4y=8 A) by constructing a table of values B) using the intercepts C) using the slope and y-intercept 3) calculate the slope of the lines that contain the following points: (-3,5)(5,6) (0,4)(-2,0) (-4,3)(8,3)

Lab 3 Calculating points on a graph 1. enter the equation into the Y= editor on your calculator 2. graph the equation 3. to calculate the y-values, press 2nd trace to open the CALC menu, and select 1:value and press ENTER. (the x and y values will be displayed at the bottom) 4. calculate the zero by pressing 2nd trace and select 2:zero, then use the arrow keys to move the cursor to the left of the zero and press ENTER. Move the cursor to the right of the zero and press ENTER. Move the cursor to the approximate location of the zero and press ENTER. The zero will be displayed at the bottom of the screen and highlighted on the graph

Calculate minimum and maximum points and intersection points Follow steps on page 85 PRACTICE: Find the zero of y=-17x+51 Find the maximum of the parabola y=-x 2 -4x+5 Find the intersection of y=-x+2 and y=-5x-1

Lab 4 changing the window and line of a graph To center the window on the vertex, locate the vertex and see how much the x and y values are moved from the origin. Go to WINDOW on your calculator and change the x min and x max and the y min and y max To zoom in on a certain area of the graph, press zoom and go to 2:zoom in To return to standard settings, go to 6:zoom standard

Changing style of a line You can change the line to a thick line, less then, greater than, or path, by moving to the left of the y= and pressing ENTER until you get to the setting you want.