Transcript Representing Proportional Relationships

Representing
Proportional
Relationships
8.EE.5 - GRAPH PROPORTIONAL RELATIONSHIPS,
INTERPRETING THE UNIT RATE AS THE SLOPE OF THE
GRAPH. COMPARE TWO DIFFERENT PROPORTIONAL
RELATIONSHIPS REPRESENTED IN DIFFERENT WAYS.
LESSON OBJECTIVES

GRAPH PROPORTIONAL RELATIONSHIPS

INTERPRET THE UNIT RATE OF A PROPORTIONAL
RELATIONSHIP AS THE SLOPE OF ITS GRAPH

UNDERSTAND THAT THE Y-INTERCEPT IS ALWAYS 0 (zero)
FOR PROPORTIONAL RELATIONSHIPS

COMPARE TWO DIFFERENT PROPORTIONAL RELATIONSHIPS
REPRESENTED IN DIFFERENT WAYS
Let’s Review!
Proportional
Relationship – the
relationship among a group of
ratios that are equivalent.
Constant of Proportionality – what
the unit rate is called in a
proportional relationship
Something to think about…..
Quantity (ex: number of pens, number of servings,
number of anything) is always represented by the
variable “x”
Unit (ex: cost, distance, measurement) is
represented by the variable “y”
What is a proportional relationship?
Suppose you and some friends plan to go to a movie and the tickets cost $8 each.
You will pay $8 for 1 ticket, $16 for 2 tickets, $24 for 3 tickets, $32 for 4 tickets, and so on.
The ratios of the total cost of the tickets to the number of tickets are all equivalent.
A group of ratios that are equivalent are in a proportional relationship. When ratios are
equivalent, they all have the same unit rate. In a proportional relationship, the unit rate is
called the constant of proportionality.
Does the data represent a proportional relationship?
What is a proportional relationship?
The unit rate
is 8. If we
plug 8 into
the equation
y = mx, our
equation is
y = 8x.
How can you use a graph to tell if a
relationship is proportional?
How can you use a graph to tell if a
relationship is proportional?
The points on the graph
are on a straight line for
both sets of data, but
only the data for the cost
of the movie tickets goes
through the origin. Only
the total cost of the
movie tickets compared
to the number of tickets is
a proportional
relationship.
Linear Equations and Proportional
Relationships
A proportional
relationship is a linear
function with slope m
and that goes through
the origin (0,0).
*Plot the following points on your
graph and connect with a straight
line: (0,0), (2,2), (4,4), (6, 6), (8,8)
Proportional Relationships
In this equation, m is the slope of the
line and is also called the unit rate.
As the x-coordinate gets larger, the
y-coordinate also gets larger at a
proportional rate.
* m represents the slope and tells us
how to move between points.
Proportional Relationships
Let’s start by finding the unit rate (also called slope).
Change in Y =
Cost
Change in X
# of Servings
Unit Rate (slope) = __________
Now, write the equation for this proportional relationship
using
y = mx.
y = ___x
Example One:
Graphing a proportional relationship equation.
Y = 2/3x
Rise = 2
Run = 3
1. Begin at the origin (0,0).
2. Move with m.
Example Two:
Let’s create a table to represent the data on the
graph.
Writing a proportional relationship equation.
m = ________
1. Find the slope using rise over run.
2. Substitute into y = mx
The equation of the line is _________________
Examples Continued…
Examples Continued…
1 yard = 3 feet
Compare the unit rates of the three restaurants and decide
which restaurant has the most soda consumption per day.
Burger Barn
Days
Number
of
Sodas
0
0
2
84
4
168
5
210
Famous Jacks
y = 39x
J.J.’s Restaurant
A) What is the slope (or unit rate) of this graph? Use at least
B) Create a table that represents the data.
two methods discussed in class and be able to explain.
Time
Distance
C) Create an equation that represents the
data.
1) At the new pet store opening, it is advertised that
the cost of 2 puppies is $80. Create a graph, table, and
equation assuming the relationship is proportional.
# of
puppies
Cost ($)
y = mx
How can you use a graph to tell if a
relationship is proportional?