Proportional Relationships and Equations
Learn about proportional relationships and equations, including the concept of constant of proportionality, graphing proportional relationships, and writing equations from tables, graphs, and verbal statements. Explore examples and master the skills needed to solve such problems easily.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Equations of proportional relationships
What weve learned.. Proportional relationships have a constant ratio, or unit rate. The constant ratio, or unit rate, can also be called the constant of proportionality. The graph of a proportional relationship is a straight line that passes through the origin.
New vocabulary.. A proportional relationship can be called a direct variation. Proportions can be represented by the equation y = kx where k is the constant of proportionality.
Writing an equation from the graph of a proportional relationship Ex. 1) The number of students that can go on a trip is proportional to the number of chaperones that are available. A) Find the constant of proportionality k, or the unit rate, of this relationship. (4, 24) students students 6 = k (3, 18) chaperones chaperone 1 (2, 12) 6 12= 6 18= 6 24= 6 1 2 1 3 1 4 1 (1, 6) B) Write an equation to represent this relationship. y = kx No. of students No. of chaperones y = 6x
Writing an equation from a table of values Ex. 2) In Mrs. McCarthy s new car, the number of miles driven is proportional to the gallons of gas used. B) Write an equation to represent this relationship. A) Find the constant of proportionality k, or the unit rate, of this relationship. miles = x y miles 30 = k y = kx gallons gallon 1 Gallons of gas used No. of miles 240= 30 180= 30 8 1 6 1 y = 30x 300= 30 360= 30 10 1 12 1
Writing an equation from a verbal statement Ex. 3) If y varies directly with x, write the equation for this relationship if y = 6 when x = 2. y k = A) Find the constant of proportionality k, or the unit rate, of this relationship. x 6= = 3 k 2 y = kx B) Write an equation to represent this relationship. y = 3x y = 3x y = 3(7) C) What is the value of y when x=7? y = 21 when x = 7
Writing an equation from a verbal statement Ex. 4) It costs $5 to send 6 packages through a certain shipping company. Consider the number of packages per dollar. y packages A) Find the constant of proportionality k, or the unit rate, for this situation. = = k x dollars 6= = 2 . 1 k 5 B) Write an equation to represent this relationship. Number of packages y = k(dollars x) y = 1.2x
