Proportions
Tables
Graphs
k=y/x and y=kx
Word Problems
100
Solve for x.
1/2 = x/52
x = 26
100
How do you determine if a table is proportional?
Solve k = y/x for all values of the table and see if they're all equal.
100
How do you determine if a graphed relationship is proportional?
It's a straight line and it goes through the origin (0,0).
100
Name the two other terms that mean the same thing as the value of k.
The constant of proportionality, the unit rate.
100
If the cost for strawberries is $1.25 per pound, which equation could be used to show the relationship between cost and pounds?
A) x = 1.25y
B) y = 125x
C) y = 1.25x
D) x = 125y
C) y = 1.25x
200
Solve for x.
3/7 = 9/x
x = 21
200
The following table is NOT proportional. Specifically explain why.
The constant of proportionality, k, was equal to 5 for all cases except the data containing 4 pies and 24 fruits. They all have to be the same to be proportional.
200
How do you determine the scale of your x-axis and y-axis?
A) Always count off by 1, no matter what.
B) Divide the amount of boxes by the highest value x and y.
C) Guess.
B) Divide the amount of boxes by the highest value x and y.
200
Which equation do we use to represent the relationship between two variables?
k = y/x OR y = kx
y = kx
200
If my car drives 82 miles per 2 gallons, which equation could be used to show the relationship between the distance traveled and gallons used?
A) x = 41y
B) y = 41x
C) x = 82y
D) y = 82x
B) y = 41x
300
Solve for m.
4/m = 6/18
m = 12
300
Is the following table proportional? Explain your reasoning.
Yes, the constant of proportionality is the same (k = 1.5) for all values.
300
Is the following graph proportional? Why or why not?
No, it's not a straight line, but it does go through the origin (0,0). Also, all values of k are different.
300
What's the constant of proportionality of the table shown? Assume the Pounds of Beef as the y values and the Cups of Broccoli as the x values.
k = y/x
k = 1 / 3/2
k = 0.6666... or 2/3
300
If Ben bought 3 video games for $179.97, how much did 1 video game cost?
k = y/x
k = 179.97/3
k = $59.99 for 1 video game
400
Solve for y.
51/y = 1275/1525
y = 61
400
What is the constant of proportionality for the following table? Complete the table using this constant.
(Google Doc Picture)
k = y/x
k = 12/3
k = 4
x = 10
y = 36
400
Is this relationship proportional? Explain.
k = y/x is the same / it's a straight line and goes through the origin (0,0).
400
Write an equation to represent the relationship between the cost ($) and the gallons of gasoline.
k = y/x
k = 10/4
k = $2.5 per gallon
y = kx
y = 2.5x
400
If Mason's family purchased 4 tickets to the Bills game for $1,146.60, how much would 9 tickets cost?
k = y/x
k = 1146.60/4
k = $286.65 for 1 ticket
y = kx
y = 286.65(9)
y = $2,579.85 for 9 tickets
500
Solve for y.
y/38 = 3293/3382
y = 37
500
Complete the following table, find the constant of proportionality, and write an equation to represent the relationship.
(Google Doc Picture)
k = y/x = 4/8 = 1/2 or 0.5
x = 10 and y = 7
y = kx
y = (1/2)x or y = 0.5x
500
What is the unit rate for the following relationship?
k = y/x
k = 15/10
k = $1.5 per square foot of carpet
500
Solve for the constant of proportionality. Then write an equation to represent the relationship between the distance traveled per time spent.
k = y/x
k = 6/8
k = 3/4 miles per minute
y = kx
y = (3/4)x
500
Muskan ordered 25 t-shirts for $187.50. If she has $30 left to spend on t-shirts, how many more t-shirts can she buy?
k = y/x
k = 25/187.50
k = 2/15 shirt for every dollar
y = kx
y = 2/15(30)
y = 4 more shirts