To help the environment and make some extra money, Dale takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dale brings in for recycling.
There is a proportional relationship between the weight (in pounds) of the cans Dale brings into the shop, x, and the amount (in dollars) the shop pays Dale, y.
x (pounds) y (dollars)
6 $3
8 $4
14 $7
16 $8
Write an equation for the relationship between x and y. Simplify any fractions.
To write an equation for the proportional relationship between x and y, we can create a ratio of y to x for each set of values provided.
For the first set of values:
y/x = 3/6
y/x = 1/2
For the second set of values:
y/x = 4/8
y/x = 1/2
For the third set of values:
y/x = 7/14
y/x = 1/2
For the fourth set of values:
y/x = 8/16
y/x = 1/2
Since the ratio of y to x is the same for all sets of values, the equation for the relationship can be written as:
y = (1/2)x
In her computer science class, Stacy is learning how to program computer games. For her final project, Stacy is creating her own multilevel game.
There is a proportional relationship between the number of levels Stacy has created for her game, x, and how long (in weeks) it took her to program them, y.
x (levels) y (weeks)
1 2
4 8
8 16
9 18
Write an equation for the relationship between x and y. Simplify any fractions.
To write an equation for the proportional relationship between x and y, we can create a ratio of y to x for each set of values provided.
For the first set of values:
y/x = 2/1
y/x = 2
For the second set of values:
y/x = 8/4
y/x = 2
For the third set of values:
y/x = 16/8
y/x = 2
For the fourth set of values:
y/x = 18/9
y/x = 2
Since the ratio of y to x is the same for all sets of values, the equation for the relationship can be written as:
y = 2x
A mysterious flying superhero known as Blue Sky protects the good citizens of Dayton. Unknown to these citizens, Blue Sky is actually mild-mannered Sebastian, a scientist in a flying suit. Before Sebastian can fly in the suit, he needs to charge its battery.
There is a proportional relationship between the number of hours Sebastian has charged his flying suit, x, and the number of hours he can fly, y.
x (hours charged) y (flight hours)
4 4
6 6
8 8
10 10
Write an equation for the relationship between x and y. Simplify any fractions.
To write an equation for the proportional relationship between x and y, we can create a ratio of y to x for each set of values provided.
For the first set of values:
y/x = 4/4
y/x = 1
For the second set of values:
y/x = 6/6
y/x = 1
For the third set of values:
y/x = 8/8
y/x = 1
For the fourth set of values:
y/x = 10/10
y/x = 1
Since the ratio of y to x is the same for all sets of values, the equation for the relationship can be written as:
y = x
Trevor wants to save up some money to buy a new smartphone, so he babysits on the weekends.
There is a proportional relationship between the time Trevor spends babysitting (in hours), x, and the amount of money he earns babysitting (in dollars), y.
x (hours) y (dollars)
1 $17
2 $34
4 $68
5 $85
Write an equation for the relationship between x and y. Simplify any fractions.
y=
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To find an equation for the relationship between x and y, we need to look at the ratio of y to x for each set of values provided.
For the first set of values:
y/x = 17/1
y/x = 17
For the second set of values:
y/x = 34/2
y/x = 17
For the third set of values:
y/x = 68/4
y/x = 17
For the fourth set of values:
y/x = 85/5
y/x = 17
Since the ratio of y to x is the same for all the sets of values, the equation for the relationship can be written as:
y = 17x
The housekeeping staff at the Weary Traveler Hotel rotates job assignments every day. Today, Victor is in charge of folding the freshly cleaned bedsheets.
There is a proportional relationship between the amount of time (in minutes) Victor spends folding, x, and the number of bedsheets he folds, y.
x (minutes) y (bedsheets)
2 4
29 58
37 74
38 76
Write an equation for the relationship between x and y. Simplify any fractions.
To find an equation for the relationship between x and y, we will calculate the ratio of y to x for each set of values:
For the first set of values:
y/x = 4/2
y/x = 2
For the second set of values:
y/x = 58/29
y/x = 2
For the third set of values:
y/x = 74/37
y/x = 2
For the fourth set of values:
y/x = 76/38
y/x = 2
Since the ratio of y to x is the same for all sets of values, the equation for the relationship is:
y = 2x