LINEAR GRAPHS AND FUNCTIONS UNIT ONE GENERAL MATHS.

Slides:



Advertisements
Similar presentations
4-4 Equations as Relations
Advertisements

Warm Ups {(2,0) (-1,3) (2,4)} Write as table Write as graph
Mathematical Modeling. What is Mathematical Modeling? Mathematical model – an equation, graph, or algorithm that fits some real data set reasonably well.
Two Variable Analysis Joshua, Alvin, Nicholas, Abigail & Kendall.
Graphing Linear Equations in Two Variables The Graph of a linear equation in two variables is the graph of all the ordered pairs (x,y) that satisfy the.
EXAMPLE 3 Write an equation for a function
Scatterplots Grade 8: 4.01 & 4.02 Collect, organize, analyze and display data (including scatter plots) to solve problems. Approximate a line of best fit.
Line of Best Fit. Age (months) Height (inches) Work with your group to make.
Thinking Mathematically Algebra: Graphs, Functions and Linear Systems 7.3 Systems of Linear Equations In Two Variables.
Linear Algebra Achievement Standard 1.4.
Topic 2: Linear Equations and Regression
12b. Regression Analysis, Part 2 CSCI N207 Data Analysis Using Spreadsheet Lingma Acheson Department of Computer and Information Science,
2-5 Using Linear Models Make predictions by writing linear equations that model real-world data.
New Seats – Block 1. New Seats – Block 2 Warm-up with Scatterplot Notes 1) 2) 3) 4) 5)
Gradient and Intercept 06 October 2015 Lesson Objective: To Plot the graphs of simple linear functions, and also find the equation of a straight line -
1 What you will learn today 1. New vocabulary 2. How to determine if data points are related 3. How to develop a linear regression equation 4. How to graph.
2-7 Curve Fitting with Linear Models LESSON PLAN Warm Up (Slide #2)
Math 10 Lesson (3) Using Data to Predict: Focus L Scatterplots.
An Introduction to Straight Line Graphs Drawing straight line graphs from their equations. Investigating different straight line graphs.
Chapter 2 – Linear Equations and Functions
Scatter Plots and Trend Lines
5.7 Scatter Plots and Line of Best Fit I can write an equation of a line of best fit and use a line of best fit to make predictions.
Unit 1: Scientific Process. Level 2 Can determine the coordinates of a given point on a graph. Can determine the independent and dependent variable when.
7-3 Line of Best Fit Objectives
Warm Ups {(2,0) (-1,3) (2,4)} 1. Write as table 2. Write as graph 3. Write as map 4. State domain & range 5. State the inverse.
UNIT 2 BIVARIATE DATA. BIVARIATE DATA – THIS TOPIC INVOLVES…. y-axis DEPENDENT VARIABLE x-axis INDEPENDENT VARIABLE.
Chapter 16 Graphs. Learning Outcomes Draw straight line graphs Draw special horizontal & vertical graphs Recognise the gradient & y-intercept from an.
Graphs and relations Construction and interpretation of graphs.
Section 1.6 Fitting Linear Functions to Data. Consider the set of points {(3,1), (4,3), (6,6), (8,12)} Plot these points on a graph –This is called a.
Algebra – Linear Functions By the end of this lesson you will be able to identify and calculate the following: 1. The gradient–intercept method.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 9.2.
Review: Writing an equation of a line Prepare to write equations for lines of best fit on scatter plots.
UNIT 2 BIVARIATE DATA. BIVARIATE DATA – THIS TOPIC INVOLVES…. y-axis DEPENDENT VARIABLE x-axis INDEPENDENT VARIABLE.
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.
Algebra – Linear Functions By the end of this lesson you will be able to identify and calculate the following: 1. Finding the equation of a straight line.
Goal: I can fit a linear function for a scatter plot that suggests a linear association. (S-ID.6)
Ch. 14 – Scatter Plots HOW CAN YOU USE SCATTER PLOTS TO SOLVE REAL WORLD PROBLEMS?
Equations of Straight Line Graphs. Graphs parallel to the y -axis All graphs of the form x = c, where c is any number, will be parallel to the y -axis.
Unit 4 Part B Concept: Best fit Line EQ: How do we create a line of best fit to represent data? Vocabulary: R – correlation coefficient y = mx + b slope.
Chapter 1 Functions and Their Graphs
4-5 Predicting with Linear Models
Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.
Objectives Fit scatter plot data using linear models.
Linear graphs and models
GENERAL MATHS – UNIT TWO
Straight Lines Objectives:
Line of Best Fit.
Solve a system of linear equation in two variables
Coordinate Planes 2.2 I can identify the paths between points on a grid or coordinate plane and compare the lengths of the paths. 3.6 I can understand.
Line of Best Fit.
GENERAL MATHS – UNIT TWO
Graphing Linear Equations
Example 1: Finding Solutions of Equations with Two Variables
USING GRAPHS TO SOLVE EQUATIONS
Know how to check all solutions
Lesson 7-4 part 3 Solving Systems by Elimination
Line of Best Fit.
4-5 Predicting with Linear Models
Function - when every x is paired to one y
Maths Unit 7 – Coordinates and real life graphs
Day 39 Making predictions
Objectives Vocabulary
Objective The student will be able to:
Warm- Up: Solve by Substitution
Unit 6 describing data/scatter plots
Bivariate Data.
Maths Unit 8 – Coordinates & Real Life Graphs
Maths Unit 9 (F) – Coordinates & Real Life Graphs
Presentation transcript:

LINEAR GRAPHS AND FUNCTIONS UNIT ONE GENERAL MATHS

INTRODUCTION TO LINEAR GRAPHS A linear function or equation is a set of ordered pairs that, when graphed, form a straight line. What does a Linear Graph look like?

DETERMINING THE EQUATION OF A STRAIGHT LINE gradient The ‘steepness’ of the line

SKETCHING A STRAIGHT LINE

(0, 1) (2, 4)

SKETCHING A STRAIGHT LINE (0, 0) (1, 2 ) (2, 4 ) (3, 6 ) (-1, -2 ) We could plot more points in this manner…..

SKETCHING A STRAIGHT LINE (0, 2) (1, 6)

SKETCHING A STRAIGHT LINE

(0, 2) (3, 0)

SKETCHING A STRAIGHT LINE (0, 4) (-2, 0)

SKETCHING A STRAIGHT LINE (0, 9) (3, 0)

SKETCHING A STRAIGHT LINE (0, 4)

NOW DO – WORKSHEET ONE

SKECTHING A STRAIGHT LINE

Enter one equation into y1, the other to y2. Highlight and drag each into the graph.

SKECTHING A STRAIGHT LINE

NOW – CHECK YOUR ANSWERS FROM WORKSHEET ONE WITH THE CLASSPAD

DETERMINING THE EQUATION OF A STRAIGHT LINE gradient The ‘steepness’ of the line

THE GRADIENT OF THE GRAPH

DETERMINING THE EQUATION OF A STRAIGHT LINE

DETERMINING THE GRADIENT AND Y-INTERCEPT Gradient = 5 y-intercept = 2 Gradient = -3 y-intercept = 7

DETERMINING THE GRADIENT AND Y-INTERCEPT Gradient = 3 y-intercept = 1 Gradient = -3 y-intercept = 4

DETERMINING THE GRADIENT GIVEN 2 POINTS

THE GRADIENT OF THE GRAPH

NOW DO – EXERCISE 10B Q1,2,3,5,6,9,10AC,12,13,16,17,19,20,21,24

DETERMINING THE EQUATION OF A LINE

DETERMINING THE EQUATION OF A STRAIGHT LINE

FINDING THE EQUATION OF A LINE GIVEN 2 POINTS

Bivariate Data can be displayed on a scatterplot. What does this look like? Two sets of data that is related is given on a table. This data is used as sets of coordinates. We plot these on an axis and use it to model relationships between variables. DISPLAYING DATA ON A SCATTERPLOT

Age (years) Foot length (cm) Example: Plot the following data on a scatterplot.

Once the data is plotted on the graph, we can add a line of best fit to model the data. How to add a line of best fit Fit the line ‘by eye’ by balancing the data points on either side of the line. DRAWING A LINE OF BEST FIT ON A SCATTERPLOT

How to add a line of best fit Fit the line ‘by eye’ by balancing the data points on either side of the line. DRAWING A LINE OF BEST FIT ON A SCATTERPLOT

FINDING THE EQUATION OF A LINE OF BEST FIT

(1.5, 65) (4, 85)

USING THE LINE OF BEST FIT TO MAKE PREDICTIONS Once we have a line of best fit, we can use this to make predictions. We can make predictions using either the graphed line – reading off the graph; or by substituting values into the linear equation and solving. Example: Estimate how many hours a student worked to obtain a grade of 80 Reading off the graph = 3.5 hours

USING THE LINE OF BEST FIT TO MAKE PREDICTIONS

RELIABILITY OF PREDICTIONS For the graphed data shown right, the data is plotted and shown in the range between the dotted lines. When making predictions, estimates that fall in this range is called INTERPOLATION – these predictions are reliable, as the line is based on data in this range. Any predictions made relating to data outside of this range is called EXTRAPOLATION – these predictions are not reliable, as the line is based on data outside of this range.

When making predictions, estimates that fall in this range is INTERPOLATION – these predictions are reliable. Any predictions made relating to data outside of this range is EXTRAPOLATION – these predictions are not reliable. eg1. If I use the line to predict what test score someone got in Physics, based on a score of 60 in Maths – would this be a reliable prediction? YES – Interpolation eg2. If I use the line to predict what test score someone got in Physics, based on a score of 25 in Maths – would this be a reliable prediction? NO – Extrapolation

NOW DO – EXERCISE 10D Q1, 2, 3, 5, 6, 8, 10, 11, 13, 14,15A, 16, 17, 18