Graphs
Tables
Equations
Unit Rates
Ratios/Proportions
100
What is the the following point on the graph called: (0,0)
Origin
100
Find the unit rate or constant of proportionality
$20 per hour
or 20/1
100
What is the constant of proportionality in this equation y = 0.5x
k = 0.5
100
It costs $28 to buy 8 bottles of shampoo. What is the unit price per bottle?
$3.50
100
Do the follwing fractions form a proportion?
2/3, 8/12
yes
200
What 2 characteristics must a graph contain in order to be proportional?
1)Go through the origin
2) Be a straight line
200
Does the table show a proportional relationship? Explain WHY using evidence to support your answer.
x 4 5 6 10
y 64 125 216 1000
No, because they have different constant of proportionalities. (need to show at least 2 pieces of data)
y/x
64/4 = 16
125/5= 25
216/6= 36
1000/10 = 100
200
Which of the following equations show a proportional relationship?
A. y = 1.25 + x
B. y =15x
C. x = 15y
D. y = 1.25x
B and D
200
It costs $14.95 to buy a 5 pound bag of coffee. It costs $23.12 to buy a 8 pound bag of coffee? Which is the better buy?
8 pound bag of coffee
200
Does the following ratios form a proportion?
1/6, 4/20
no
300
From the following 2 points on a graph what is the constant of proportionality? (1, 3) and (2,6)
3
300
Jean has $280 in her savings account. Starting next week, she will deposit $30 in her account every week. Is the amount of money in her account proportional to the number of weeks?
No - already having $280 in her savings account makes this relationship not proportional as seen by the constants of proportionalities.
300
A recipe calls for 3 ounces of flour, y, for every 2 ounces of sugar, x. Write an equation that represents the proportional relationship between the number of ounces of flour to the number of ounces of sugar.
y= 3/2x
or y= 1.5x
or y = 1 1/2x
300
Amy rides her bike 4 miles in 3/4 hours. How many miles can she ride in 1 hour?
5 1/4 miles
300
Solve the following proportion: 5/12 = 15/x
36
400
What is the constant of proportionality for the graph with the following points? (4,2) (6,3) (8, 4)
1/2
400
Do the two tables show the same proportional relationship between x and y? Explain WHY or WHY NOT.
Table 1
(x) 500 750 1000
(y) 1250 1875 2500
Table 2
(x) 3 4 5
(y) 4.2 5.6 7
No - the first one has a constant of proportionality of 2.5 and the second one has a constant of proportionality of (y/x = 1.4 , 2.5, 1.4...)
400
An engineer makes different-size samples of a new material. The table shows volumes and the related masses.
x represents the volume in cubic centimeters and y represents the mass in grams.
(x) (y)
9 90
14 140
25 250
What would the mass of 100 cubic centimeters of the material be?
1000 grams
The equation of the table is y = 10x
You need to find the mass which is the y, so plug 100 in for x and multiply 10 by 100.
400
Amy can paint 1/2 a room is 1/4 of an hour. How much can she paint in 1 hour?
2 rooms
400
Workdays to leisure days come in a ratio of 5 to 2 If a man take 14 leisure days, How many work days did he have to work?
35
500
3
500
Decide whether the table shows a proportional relationship between x and y.
(x) (y)
30 150
1/6 5/6
2/15 2/3
Yes- constant of proportionality is 5
500
For every 3 lemons you buy at a farm stand, the total cost increases by $1.80. Using the chart below, determine how many lemons you could get if you spent $16.20
x- number of lemons
y - $ in dollars
(x) (y)
4 $2.40
7 $4.20
15 $9
18 $10.80
27 lemons -
Using the equation
y = 0.6x plus $16.20 in for y and solve for x.
16.20 = 0.6x
0.6 0.6
27 = x
500
John can run 3/4 of a mile in 1/3 of an hour. How far can he run in 2 hour?
4 1/2 miles
500
The ratio of people to square miles in Alaska is 5 to 1. How many people would live on 250 square miles?
1250 people