Transcript Tuesday, Oct 30 - Xenia Community Schools

5 Minute Check
Complete in your notes.
MegaMart collects a sakes tax equal to 1/16
of the retail price of each purchase. The tax
is sent to the government.
1. Is the amount of tax collected proportional
to the cost of an item before the tax is
collected? Explain.
2. Is the amount of tax collected proportional
to the cost of an item after tax has been
added? Explain.
5 Minute Check
Complete in your notes.
MegaMart collects a sakes tax equal to 1/16
of the retail price of each purchase. The tax
is sent to the government.
1. Is the amount of tax collected proportional
to the cost of an item before the tax is
collected? Explain.
5 Minute Check
Complete in your notes.
MegaMart collects a sakes tax equal to 1/16
of the retail price of each purchase. The tax
is sent to the government.
1. Is the amount of tax collected proportional
to the cost of an item before the tax is
collected? Explain.
5 Minute Check
Complete in your notes.
MegaMart collects a sakes tax equal to 1/16
of the retail price of each purchase. The tax
is sent to the government.
2. Is the amount of tax collected proportional
to the cost of an item after tax has been
added? Explain.
5 Minute Check
Complete in your notes.
MegaMart collects a sakes tax equal to 1/16
of the retail price of each purchase. The tax
is sent to the government.
2. Is the amount of tax collected proportional
to the cost of an item after tax has been
added? Explain.
Monday, Jan 12
Lesson 7.1.5
Graph Proportional Relationships
Graph Proportional Relationships
Objective: To identify proportional
relationships by graphing on the coordinate
plane.
You will need your graph paper for today’s
lesson.
Graph Proportional Relationships
Another way to determine whether two
quantities are proportional is to graph the
quantities on the coordinate plane. If the
graph of the two quantities is a straight line
through the origin, then the two quantities
are proportional.
Graph Proportional Relationships
The slowest animal on Earth is the three sloth. It
moves at a speed of 6 feet per minute. Determine
whether the number of feet the sloth moves is
proportional to the number of minutes it moves by
graphing on the coordinate plane. Explain your
reasoning.
Determining Proportions by Graphing
Step 1 – Make a table.
Graph Proportional Relationships
The slowest animal on Earth is the three sloth. It
moves at a speed of 6 feet per minute. Determine
whether the number of feet the sloth moves is
proportional to the number of minutes it moves by
graphing on the coordinate plane. Explain your
reasoning.
Determining Proportions by Graphing
Step 1 – Make a table.
Graph Proportional Relationships
The slowest animal on Earth is the three sloth. It
moves at a speed of 6 feet per minute. Determine
whether the number of feet the sloth moves is
proportional to the number of minutes it moves by
graphing on the coordinate plane. Explain your
reasoning.
Determining Proportions by Graphing
Step 2 – Graph the coordinates.
Graph Proportional Relationships
The slowest animal on Earth is the three sloth. It
moves at a speed of 6 feet per minute. Determine
whether the number of feet the sloth moves is
proportional to the number of minutes it moves by
graphing on the coordinate plane. Explain your
reasoning.
Determining Proportions by Graphing
Step 2 – Graph the coordinates.
Graph Proportional Relationships
The slowest animal on Earth is the three sloth. It
moves at a speed of 6 feet per minute. Determine
whether the number of feet the sloth moves is
proportional to the number of minutes it moves by
graphing on the coordinate plane. Explain your
reasoning.
If the graph is a straight line and
passes through the origin, it is
Proportional.
Is this graph proportional?
Graph Proportional Relationships
James earns $5 an hour babysitting. Determine
whether the amount of money he earns is
proportional to the number of hours he babysits
by graphing by on the coordinate plane. Explain
your reasoning.
Do this on your own.
Graph Proportional Relationships
James earns $5 an hour babysitting. Determine
whether the amount of money he earns is
proportional to the number of hours he babysits
by graphing by on the coordinate plane. Explain
your reasoning.
Since the graph is a straight
line and passes through the
origin, the time-tomoney is proportional.
Graph Proportional Relationships
Determine whether the number of pizzas is
proportional to the amount of cheese by graphing
by on the coordinate plane. Explain your
reasoning.
Do this on your own.
Graph Proportional Relationships
Determine whether the number of pizzas is
proportional to the amount of cheese by graphing
by on the coordinate plane. Explain your
reasoning.
(sometimes you may need to
extend the line to see if it
passes through the origin)
Since the graph is a straight
line and passes through the
origin, the pizzas-to- cheese is proportional.
Graph Proportional Relationships
The cost of renting a video game from Games, Inc
is shown in the table. Determine whether the cost
is proportional to the numbers of games rented by
graphing by on the coordinate plane. Explain
your reasoning.
Do this on your own.
Graph Proportional Relationships
The cost of renting a video game from Games, Inc
is shown in the table. Determine whether the cost
is proportional to the numbers of games rented by
graphing by on the coordinate plane. Explain
your reasoning.
Since the graph is a straight
line but does not pass through the
origin, the cost-togame is nonproportional.
Graph Proportional Relationships
Which batting cage represents a proportional
relationship between the number of pitches thrown
and the cost? Explain your reasoning.
Graph Proportional Relationships
Which batting cage represents a proportional
relationship between the number of pitches thrown
and the cost? Explain your reasoning.
Softball Plus is a straight
line, but does not pass
through the origin. It is
nonproportional.
Fun Center is a straight
line, but does pass
through the origin. It is
proportional.
Graph Proportional Relationships
A proportion is an equation stating two rates
or ratios are equivalent.
Graph Proportional Relationships
A proportion is an equation stating two rates
or ratios are equivalent.
Two rates or ratios are equivalent if their
cross products are equal.
Graph Proportional Relationships
Two rates or ratios are equivalent if their
cross products are equal.
6 · 4 = 24
Graph Proportional Relationships
Two rates or ratios are equivalent if their
cross products are equal.
6 · 4 = 24
8 · 3 = 24
Since the cross products are equal, they are
equivalent.
Graph Proportional Relationships
Is this a true statement?
4
5
2
3
Graph Proportional Relationships
Is this a true statement?
4
5
2
3
5 · 2 = 10
4 · 3 = 12
It is not a true statement
Graph Proportional Relationships
Is this a true statement?
7
9
10
13
Graph Proportional Relationships
Is this a true statement?
7
9
10
13
9 · 10 = 90
7 · 13 = 101
It is not a true statement
Graph Proportional Relationships
Is this a true statement?
12
15
40
50
Graph Proportional Relationships
Is this a true statement?
12
15
40
50
15 · 40 = 600
12 · 50 = 600
It is a true statement
Graph Proportional Relationships
Is this a true statement?
16
21
12
17
Graph Proportional Relationships
Is this a true statement?
16
21
12
17
21 · 12 = 252
16 · 17 = 272
It is not a true statement
Graph Proportional Relationships
Johanna’s parents give her $10 per week for lunch money.
The greenhouse temperatures at certain times are
shown in the table. The greenhouse maintains
temperatures between 65°F and 85°F. Suppose the
temperature increases as a constant rate. Create a
graph of the time and temperatures at each hour
from 1PM and 8PM. Is the relationship proportional?
Explain.
Graph Proportional Relationships
Johanna’s parents give her $10 per week for lunch money.
The greenhouse temperatures at certain times are shown in
the table. The greenhouse maintains temperatures between
65°F and 85°F. Suppose the temperature increases as a
constant rate. Create a graph of the time and temperatures
at each hour from 1PM and 8PM. Is the relationship
proportional? Explain.
Since the straight line does not pass
through the origin, it is not
proportional.
Proportional and Nonproportional
Relationships
Agenda Notes
Homework –
Homework Practice 7.1.5
Due Tuesday, Jan 13
Mid-Chapter Quiz – Tuesday, Jan 13
Chapter 7.1 Test - Friday, Jan 16