Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. MATH 108 Section 2.1-2.2 Coordinate Plane and Graphs.

Slides:



Advertisements
Similar presentations
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.
Advertisements

Copyright © 2010 Pearson Education, Inc. All rights reserved Sec The Rectangular Coordinate System.
Graphs & Models (P1) September 5th, I. The Graph of an Equation Ex. 1: Sketch the graph of y = (x - 1)
Rectangular Coordinate System
Finding the Intercepts of a Line
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.
X y 1 st Quadrant2 nd Quadrant 3 rd Quadrant4 th Quadrant 13.1 – The Rectangular Coordinate System origin x-axis y-axis.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec
Section 1.1 The Distance and Midpoint Formulas. x axis y axis origin Rectangular or Cartesian Coordinate System.
2 Graphs and Functions © 2008 Pearson Addison-Wesley. All rights reserved Sections 2.1–2.4.
Digital Lesson Graphs of Equations. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The graph of an equation in two variables x and.
Section 1.1 The Distance and Midpoint Formulas. x axis y axis origin Rectangular or Cartesian Coordinate System.
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.
Lesson 1-1 Points and Lines. Objective: To find the intersection of two lines and to find the length and the coordinates of the midpoint of a segment.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2013 Pearson Education, Inc. All rights reserved Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing.
Copyright © 2013 Pearson Education, Inc. All rights reserved Section 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing.
Quadrant II (x 0) Quadrant I (x > 0, y>0) ( -5, 3) x-axis Origin ( 0,0 ) Quadrant IV (x>0, y
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.1 The Distance and Midpoint Formulas.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 11.4 The Hyperbola.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Graphing Equations and Inequalities.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3-1 Graphs and Functions Chapter 3.
8.1 The Rectangular Coordinate System and Circles Part 1: Distance and Midpoint Formulas.
coordinates, lines and increment
Copyright © 2009 Pearson Education, Inc. CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions,
Graphing Equations of Lines Using x- and y-Intercepts.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.3 Lines.
OBJECTIVES Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Graphs of Equations Sketch a graph by plotting points. Find the.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Section 1Chapter 3. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives The Rectangular Coordinate System Interpret a line graph.
Section 8.2 Points, Lines and Their Graphs. Vocabulary Graph/Plot – an ordered pair or a point in a numbered plane Horizontal Axis – x-axis Vertical Axis.
Section 1.1 Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations.
Section 2.4 – Circles Circle – a set of points in a plane that are equidistant from a fixed point.
Section 1.1 Introduction to Graphing Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Slide 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. The Rectangular Coordinate System and Paired Data Section8.3.
Do now Solve 4x 4 -65x (3, ∞) Write as an inequality Sketch Bound or unbound?
1.1 and 1.5 Rectangular Coordinates and Circles Every man dies, not every man really lives. -William Wallace.
Graphing Linear Equations
Section 1.2 Graphs of Equations In Two Variables; Intercepts; Symmetry.
Chapter 3 Section 1 Copyright © 2011 Pearson Education, Inc.
X y Cartesian Plane y axis x axis origin René Descartes ( ) Points and their Coordinates.
Digital Lesson Graphs of Equations. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The graph of an equation in two variables x and.
1.1) RECTANGULAR COORDINATES Pg 9 # 1- Do Now!. Coordinate Plane  Label: x, y-axis, origin, quadrants  Plot points.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 1.1 The Distance and Midpoint Formulas.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Graphing Linear Equations
Graphing Linear Equations
Section 9.1 Polar Coordinates
Section 2.4 Circles Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Rectangular Coordinates;
Graphs, Linear Equations, and Functions
Introduction to Graphing
Cartesian Coordinate System
Coordinate Plane Sections 1.3,
Chapter 1 Graphs, Functions, and Models.
The Distance and Midpoint Formulas
Section 1.5 Circles Copyright © 2013 Pearson Education, Inc. All rights reserved.
Chapter 3 Graphs and Functions.
2.3 Graph Equations of Lines
Introduction to Graphing
The Distance and Midpoint Formulas
Straight Lines and Linear Functions
Warm-Up
Rectangular Coordinates; Introduction to Graphing Equations
The Distance & Midpoint Formulas
Digital Lesson Graphs of Equations.
Presentation transcript:

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. MATH 108 Section Coordinate Plane and Graphs

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. x axis y axis origin Rectangular/ Cartesian Coordinate System/ Plane

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Let's plot the point (6,4) (-3,-5) (0,7) Let's plot the point (-6,0) (6,4) (-6,0) Let's plot the point (-3,-5)Let's plot the point (0,7)

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Quadrant I x > 0, y > 0 Quadrant II x 0 Quadrant III x < 0, y < 0 Quadrant IV x > 0, y < 0

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find the distance d between the points (2, - 4) and ( -1, 3).

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find the midpoint of the line segment from P 1 = (4, -2) to P 2 = (2, -5). Plot the points and their midpoint.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.2 Graphs of Equations

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find the slope m and y-intercept b of the equation -12x + 3y = 6. Graph the equation. Find the slope m and y-intercept b of the equation - -x + 4y + 5 = 3. Graph the equation.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 13 © 2010 Pearson Education, Inc. All rights reserved Definitions Any point where a graph intersects the x-axis has the form (a, 0). The number a is called an x-intercept of the graph. y = 0 Similarly, any point where a graph intersects the y-axis has the form (0, b), and the number b is called a y-intercept of the graph. x = 0

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. PROCEDURE FOR FINDING THE INTERCEPTS OF A GRAPH Step 1To find the x-intercepts of an equation, set y = 0 in the equation and solve for x. Step 2To find the y-intercepts of an equation, set x = 0 in the equation and solve for y. 14 © 2010 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Graph the linear equation 3x + 2y = 6 by finding its intercepts.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Write the standard form of the equation of the circle with radius 4 and center (2, -4).

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Change from general form to standard form (by completing the square): x 2 + y 2 – 8x + 4y – 5 = 0 x 2 + y 2 + 2x + 6y – 26 = 0