Linear relations
Download as PPT, PDF1 like2,537 views
This document discusses linear relations and how to represent relationships between two variables with tables, graphs, and equations. It explains that a linear relation produces a straight line when graphed and can be represented by an equation of the form y = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate how to determine the equation from a table of values and vice versa, as well as how to graph lines from equations or data tables.
Linear relations
- 1. Linear RelationsLinear Relations Reporter: Reymart A. Bargamento
- 2. Linear Relations • In this unit, we are going to look at relationships between variables. • These relationships, when graphed, produce straight lines. – We call these relationships LINEAR RELATIONS. • Every line is made up of an infinite number of coordinates (x, y). When the coordinates are close enough together they look like a line! • Before we can graph a line, we must be able to determine the coordinates that make up that line. – We can do this by using a table of values.
- 3. x y What do the arrows mean on this line? How many other coordinates are on this line? What do the arrows mean on this line? How many other coordinates are on this line? ( _____ , _____ ) ( _____ , _____ ) ( _____ , _____ ) ( _____ , _____ ) ( _____ , _____ ) ( _____ , _____ )
- 4. x y -1 -1 0 0 1 1 2 2 3 3 Can you determine an equation that relates x and y?Can you determine an equation that relates x and y? What can you say about the relationship between x and y. What can you say about the relationship between x and y. The table of values below shows a relationship between 2 variables. Create graphs using the table of values. The table of values below shows a relationship between 2 variables. Create graphs using the table of values.
- 5. Can you determine an equation that relates x and y?Can you determine an equation that relates x and y? What can you say about the relationship between x and y. What can you say about the relationship between x and y. Try this one… create a graph from this table of values…Try this one… create a graph from this table of values… x y 0 -5 1 -2 2 1 3 4 4 7
- 6. 2 2y x= + Sometimes we are just given an equation and asked to graph it. Here’s an example: Graph : Graph : x y -1 0 1 2 How can we get coordinates by using this equation? How can we get coordinates by using this equation?
- 7. Let’s look at it a bit further… • How many points do you need in order to graph a line? • Why is it a good idea to have more than the minimum number of points? • From your graph, determine 2 more points on the line. By using the equation, PROVE they are on the line. 2 2y x= +
- 8. Example (if needed) • The first 4 rectangles in a pattern are shown below. The pattern continues. Each small square has a side length of 1 cm. • The perimeter of the rectangle is related to the rectangle number. • Express the relationship between the perimeter and the rectangle number using words, a table of values, an equation and a graph. #2 #4#3#1
- 9. Using a Table of Values Rectangle Number, n Perimeter, p (cm) 1 2 3 4 4 2(2) 8+ = 4 2(3) 10+ = “As the rectangle number increases by 1, the perimeter increases by 2 cm.” “As the rectangle number increases by 1, the perimeter increases by 2 cm.” 4 2(1) 6+ = 4 2(4) 12+ = What is an equation that represents this data? What is an equation that represents this data? 2 4P n= +
- 10. Using a Graph Graph of P against n 6 8 10 12 0 2 4 6 8 10 12 14 0 1 2 3 4 5 n (number of squares) P(perimeter) Clearly label each axis (in this case P and n). Also, label your scale (go up by 1’s, 2’s, 5’s, etc.) Clearly label each axis (in this case P and n). Also, label your scale (go up by 1’s, 2’s, 5’s, etc.) Don’t forget your title!Don’t forget your title! To determine whether or not to connect the points, ask yourself if the points in between ‘matter’. To determine whether or not to connect the points, ask yourself if the points in between ‘matter’. Independent variable is on the x- axis Independent variable is on the x- axis Dependent variable is on the y-axisDependent variable is on the y-axis