Constant of Proportionality - Definition & Examples
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- (Video) Variation by mathman1024 This video by mathman1024 explains direct variation, also known as direct proportionality. Summary\large{\text{Summary}}Summary Variation or pro…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Sarah Walker, Jonathan Heller, Anusha Rahman
- What are Direct Proportions Direct proportionality, or direct variation, is a special relationship between two variables. When one variables changes, the other changes proportio…
By Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman
- The Constant of Proportionality We can use the constant of proportionality, kkk, when solving direct variation problems. kkk doesn't change in one equation. kkk signifies the re…
By Anusha Rahman
Problems 42
- If yyy is directly proportional to xxx, where y=3xy=3xy=3x, what is the constant of variation?
- If yyy is directly proportional to xxx, with the equation y=−6xy=-6xy=−6x, what is the constant of variation?
- In the equation (y+4.5)=32(x+3)(y+4.5)=\frac{3}{2}(x+3)(y+4.5)=23(x+3), is yyy is directly proportional to xxx? If so, what is the constant of variation, as a decimal?
- Is yyy is directly proportional to xxx? If so, what is the constant of variation?
- What is the constant of variation, as a decimal?
- True or False\text{True or False}True or False === A directly proportional equation y=kx+cy=kx+cy=kx+c can have a nonzero constant ccc.
- In which equation is yyy directly proportional to xxx?
- In which equation is yyy directly proportional to xxx?
- The table above represents a directly proportional relation, y=kxy = kxy=kx, between yyy and xxx. What is kkk?
- A bakery sells 555 cakes for every dozen cupcakes they sell. If by the end of the day the bakery has sold 606060 cupcakes, how many cakes did they sell?
- A cardboard company makes and sells cardboard boxes. The boxes are sold in bundles of 454545 boxes for 303030 dollars. Which equation below shows how many nnn boxes a person can…
- The Expii Zoo has a dozen monkeys in their primate exhibit. If the group of monkeys eats an average of 606060 bananas a day, write an equation for how many bananas, bbb, the Zoo…
- At a middle school, a class is on average 20 students. A teacher teaches 6 classes in a day. Using the variables yyy, years, and sss, students, write an equation for how many st…
- At a middle school, a class is on average 20 students. A teacher teaches 6 classes in a day. 1 year has 180 school days in it. How many students will a teacher teach after 35 ye…
- At a middle school, a class is on average 20 students. A teacher teaches 6 classes in a day. 1 year has 180 school days in it. Using the variables yyy, years, and ccc, classes, …
- An office of 777 people drinks 333 pots of coffee in a day. Each pot of coffee has 121212 cups in it. Write an equation for how many cups of coffee, ccc, the office will drink i…
- Which of the following equations do NOT describe directly proportional relationships between xxx and yyy?
- Using the graph above, select the functions of the form f(x)=kxf(x) = kxf(x)=kx.
- Which of the following options represents a direct relationship between xxx and yyy? Here, kkk is a constant.
- If y=2xy = 2xy=2x, then...
- If y=2+xy = 2 + xy=2+x, then...
- Which of the following is the constant of proportionality in the equation: 3y=6x3y=6x3y=6x
- Select the values that cannot be the constant of proportionality.
- True or False\text{True or False}True or False === Directly proportional equations always have a yyy-intercept of zero.
- True or False\text{True or False}True or False === If you get paid hourly then the amount of money you make is directly proportional to the hours you worked.
- True or False\text{True or False}True or False === Fahrenheit and Celsius are directly proportional to one another. The conversion equation is: F=95C+32F=\frac95 C+32F=59C+32
- True or False\text{True or False}True or False === The constant of proportionality for a directly proportional line is just yx\frac yxxy.
- Would the table above represent a direct proportion?
- How long does the walk need to be to maximize its happiness? Round to the nearest minute.
- Let xxx be directly proportional to yyy. If x=6x=6x=6 when y=10y=10y=10, find yyy when x=9x=9x=9.
- Let xxx be directly proportional to yyy. If x=ax=ax=a when y=by=by=b, write an equation for yyy in terms of xxx.
- The number of pages you read and and the time it took you to read them are directly proportional. If it takes you 30 minutes to read 75 pages, how long will it take you to read …
- If 3 people go out to eat, the check comes out to be \85. How many people go out to eat if the check comes out to be \765, with the same average price per person?
- Let xxx and yyy be directly proportional. If x=10x=10x=10 when y=12y=12y=12 what will xxx be when y=42y=42y=42?
- Let xxx and yyy be directly proportional. If x=18x=18x=18 when y=234y=234y=234 what will yyy be when x=42x=42x=42?
- What is the relationship between the hours you worked at your part time job and amount of money you are making from the job?
- Jane put out a cup during a rain storm to measure the rate of rainfall. During the first hour, Jane observed 7.87.87.8 mm of rain. Later, Jane observed that there are 15.615.615…
- A ball is dropped from a high place. The relationship between the distance the ball falls, denoted ddd, and the time take to fall, denoted ttt, is expressed below: d=4.9t2d=4.9 …
- yyy is directly proportional to xxx. When xxx is 444, yyy is 808080. What is yyy when x=10x=10x=10?
- Water is being pumped into a swimming pool at a constant rate. After the first hour, 116\frac{1}{16}161 of the pool is filled. After the second hour, 18\frac{1}{8}81 of the po…
- Three friends go out to dinner. It is difficult to split the bill, so Greg paid for everything. The bill was 73 dollars, but with tip Greg paid 91.25 dollars. Casey's food and d…
- Kaitlyn spends 40 dollars on groceries every week. In addition, she spends about 25 dollars on coffee, snacks and eating out every week. Let FFF be the money she spends on food …