The Rectangular Coordinate System and Paired Data Section 3.1.

Slides:



Advertisements
Similar presentations
Objective: Use slope-intercept form and standard form to graph equations. 2.4 Quick Graphs of Linear Equations.
Advertisements

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
Graphing Equations: Point-Plotting, Intercepts, and Symmetry
4.5 Graphing Linear Equations
Sullivan Algebra and Trigonometry: Section 2.2 Graphs of Equations Objectives Graph Equations by Plotting Points Find Intercepts from a Graph Find Intercepts.
Quadrant II (x 0) Quadrant I (x > 0, y>0) ( -5, 3) x-axis Origin ( 0,0 ) Quadrant IV (x>0, y
Rectangular Coordinate System
Finding the Intercepts of a Line
X y (x,y) x - coordinate y - coordinate. How are coordinates helpful?
Learn to locate and graph points on the coordinate plane.
X y 1 st Quadrant2 nd Quadrant 3 rd Quadrant4 th Quadrant 13.1 – The Rectangular Coordinate System origin x-axis y-axis.
Graphing on a Coordinate Plane
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Plot points and lines on a coordinate plane. 1.4 Graphing With Coordinates.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec
Rectangular Coordinate System
3.1 – Paired Data and The Rectangular Coordinate System
Section 1.1 The Distance and Midpoint Formulas. x axis y axis origin Rectangular or Cartesian Coordinate System.
Graphing Linear Equations Section 1.2. Lehmann, Intermediate Algebra, 3ed Section 1.2 Consider the equation. Let’s find y when So, when, which cab be.
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.
In this lesson we will explore x and y intercepts of linear equations.
Bellwork. Objective 1 The student will be able to: graph ordered pairs on a coordinate plane.
Quadrant II (x 0) Quadrant I (x > 0, y>0) ( -5, 3) x-axis Origin ( 0,0 ) Quadrant IV (x>0, y
Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Graphs and Graphing Utilities.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 10 Graphing Equations and Inequalities.
Rectangular Coordinate System Created by Laura Ralston.
coordinates, lines and increment
1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Graphing Linear Equations and Inequalities CHAPTER 4.1The Rectangular.
Graphing Linear Equations Section 1.2. Lehmann, Intermediate Algebra, 3ed Section 1.2 Consider the equation. Let’s find y when So, when, which can be.
Graphing Equations of Lines Using x- and y-Intercepts.
Martin-Gay, Beginning Algebra, 5ed 22 Linear Equation in Two Variables A linear equation in two variables is an equation that can be written in the form.
What is the x-intercept? The x-coordinate of a point where the graph crosses the x- axis. What is the y-intercept? The y-coordinate of a point where a.
Graphing on the Coordinate Plane
Graphing Linear Equations Linear Equations can be graphed on a Cartesian Coordinate system Free powerpoints at
Objective: I can analyze the graph of a linear function to find solutions and intercepts.
The x-intercept of a line is the point (a,0) where the line intersects the x-axis. x and y Intercepts (a,0)
Chapter 7 Section 1 The Cartesian Coordinate System and Linear Equations in Two Variables.
3.1 READING GRAPHS; LINEAR EQUATIONS IN TWO VARIABLES.
Section 1Chapter 3. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives The Rectangular Coordinate System Interpret a line graph.
COORDINATE PLANE Math 7.
The Rectangular Coordinate System and Paired Data Section 8.3.
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 2.1 Graphs  Points & Ordered Pairs (x,y)  Quadrants I II III IV  Solutions to Equations x-intercepts  Nonlinear Equations 12.1.
Rectangular Coordinate System In pre-algebra, we used number lines to plot numbers and equations and inequalities of 1 variable (x = -3, x one-dimensional)
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 3.2 Graphing Linear Equations Using Intercepts Copyright © 2013, 2009, 2006 Pearson Education,
Chapter 1 Graphing. § 1.1 Reading Graphs and the Rectangular Coordinate System.
The Coordinate Plane 1.10 p. 50 Learn to locate and graph points on the coordinate plane, name the coordinates of points, and identify the quadrants.
3.1 Reading Graphs and the Rectangular Coordinate System.
Bell Work Simplify each expression 6x + (5x – 8) – 9 – (12 – 3x) 4(6n + 9) – 10n Solve the 2-step equation 8 + 2b = – 2r = 8 Answers 11x –
Graphing Equations Chapter 3.1. Objectives Plot ordered pairs Determine whether an ordered pair of numbers is a solution to an equation in two variables.
Graphing Linear Equations in Two Variables Section 8.4.
Rectangular Coordinate System In algebra, we used number lines to plot numbers and equations and inequalities of 1 variable (x = -3, x one-dimensional)
Slide 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. The Rectangular Coordinate System and Paired Data Section8.3.
Graphing Linear Equations
Chapter 3 Section 1 Copyright © 2011 Pearson Education, Inc.
Warm-Up Determine the coordinates of each point in the graph below. y
Holt Algebra Using Intercepts Warm Up 1. 5x + 0 = –10 Solve each equation. – – = 0 + 3y x + 14 = –3x –5y – 1 = 7y + 5.
Graphing Linear Equations In Standard Form Ax + By = C.
Graphing Linear Equations In Standard Form Ax + By = C.
5-1 The Coordinate Plane Introduction. Coordinate Graph.
WARM UP 1.Evaluate when x = -3 and y = Evaluate (2x)² when x = 5. 5 Minutes Remain x - y 4.
Objective The student will be able to: graph ordered pairs on a coordinate plane.
Chapter-4(part 1) Graphing Linear Equations and Functions By: Donna, Fannie, Ashley and Nick.
Chapter 3 Graphs and Functions. § 3.1 Graphing Equations.
Integrated Mathematics. Objectives The student will be able to:: 1. graph linear equations. 2. write equations in point- slope form.
Graphs and Applications of Linear Equations
Graphing in the Coordinate Plane
Graphing Linear Equations
Warm-Up
Presentation transcript:

The Rectangular Coordinate System and Paired Data Section 3.1

origin quadrant I quadrant II quadrant III quadrant IV The Rectangular Coordinate System x-axis y-axis (0,0) 2

Plotting Points x y 2 (4,3) 3

In general, to plot the ordered pair (x,y), start at the origin. Next, right if x is positive, left if x is negative up if y is positive, down if y is negative move units left or right and then move units up or down. move x units left or right and then move y units up or down. (x,y)(x,y) 4 Martin-Gay, Prealgebra, 5ed

Since the first number, or x-coordinate, x-coordinate, of an ordered pair is associated with the x-axis, x-axis, it tells how many units to move left or right. Similarly, the second number, or or y-coordinate, tells how many units to move up or down. Helpful Hint 5 Martin-Gay, Prealgebra, 5ed

Plot,,,,, and. Plot (2,1), (- 3,4), (5,0), (0,- 2), (1,- 3), and (- 4,- 5) x y (2,1) (- 3,4) (5,0) (- 4,- 5) (0,- 2) (1,- 3) 6

Remember that each point point in the rectangular coordinate system corresponds to exactly one ordered ordered pair and that each ordered pair pair corresponds to exactly one point. Helpful Hint 7 Martin-Gay, Prealgebra, 5ed

If an ordered pair has a y-coordinate y-coordinate of 0, its graph lies on the x-axis. x-axis. If an ordered pair has an x-coordinate x-coordinate of 0, its graph lies on the y-axis. Order Order is the key word in ordered pair. The first value always corresponds to the x-value x-value and the second value always corresponds to the y-value. Helpful Hint 8 Martin-Gay, Prealgebra, 5ed

Completing Ordered Pair Solutions An equation in two variables, such as 3x 3x + y = 9, has solutions consisting of two values, one for x and one for y.y. x 1y 6 For example, x = 1 and y = 6 is a solution of 3x + y = 9, because, if x is replaced with 1 and y is replaced with 6, we get a true statement. xy 3x + y = 9 1 3(1) + 6 = 9 ? 9 = 9 True The solution x = 1 and y = 6 can be written as (1,6), an ordered pair of numbers. 9 Martin-Gay, Prealgebra, 5ed

The x-intercept of the graph of an equation is the x-coordinate of the point where the graph crosses the x-axis. The y intercept is defined similarly. 10

Graph each of the following linear equations by first finding the intercepts. 5x - 3y= 15 (0, ) x = 0 Let x = 0 and solve for y. x5x x5x -3 y = (0) - 3y 3y = y 3y = 6 y = - 2 (, 0) y = 0 Let y = 0 and solve for x. 5x 5x - 3y 3y = 15 5x 5x – 3(0) = 15 5x 5x = x = 3 The y-intercept is (0,- 2).The x intercept (3,0). 11