Lesson 5 Homework Practice Direct Variation Answer Key

[Nia Reyome]

Lesson 5 Homework Practice Direct Variation Answer Key
Are you struggling with direct variation problems in algebra? Do you want to learn how to identify, write, and use direct variation equations to find missing values? If so, you are in the right place. In this article, we will explain what direct variation is, how to recognize it, and how to solve it. We will also provide you with a lesson 5 homework practice direct variation answer key, so you can check your answers and improve your skills.



Lesson 5 Homework Practice Direct Variation Answer Key

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What is Direct Variation?
Direct variation is a type of linear relationship between two variables, where one variable changes by the same factor as the other. For example, if x varies directly with y, then whenever x increases or decreases, y also increases or decreases by the same amount.


Direct variation can be represented by the formula y = kx, where k is called the constant of variation or the constant of proportionality. This formula tells us that y is equal to x multiplied by some constant factor k.


Direct variation can also be represented by a table of values or a graph of two variables. If the ratio of the values is constant, then the variables vary directly. If the graph is a straight line that passes through the origin (0,0), then the variables vary directly.


How to Identify Direct Variation?
To identify direct variation, we can use one of these methods:



Look at a table of values for two variables. If the ratio of the values is constant, then the variables vary directly. For example, look at this table:


x36912
y15304560


If we divide y by x for each pair of values, we get the same result: 5. This means that y varies directly with x.

Look at a graph of two variables. If the graph is a straight line that passes through the origin (0,0), then the variables vary directly. For example, look at this graph:





The graph shows a straight line that passes through the origin, so it represents a direct variation.

How to Write an Equation for Direct Variation?
To write an equation for direct variation, we can use the formula y = kx, where k is the constant of variation. To find the value of k, we can use any pair of values for x and y that satisfy the direct variation. For example, using the table above, we can plug in x = 3 and y = 15 into the formula and solve for k:



y = kx
15 = k(3)
15/3 = k
5 = k


So, the equation for this direct variation is y = 5x.






How to Use Direct Variation to Find Missing Values?
To use direct variation to find missing values, we can plug in the given values into the equation and solve for the unknown variable. For example, using the equation y = 5x, we can find y when x = 10:



y = 5x
y = 5(10)
y = 50


Or, we can find x when y = 25:



y = 5x
25 = 5x
25/5 = x
5 = x


Lesson 5 Homework Practice Direct Variation Answer Key
Now that you know how to work with direct variation, you can try some homework practice problems. Here are some questions from lesson 5 homework practice direct variation worksheet, along with their answers and explanations.




If y varies directly with x and y = -8 when x = -4, determine y when x = -12.

Answer: To find y when x = -12, we can use the formula y = kx and plug in the given values:

y = kx
-8 = k(-4)
-8/-4 = k
2 = k
y = kx
y = 2(-12)
y = -24


So, y = -24 when x = -12.

The number of hours a person studies varies directly with their test score. If a person studies 6 hours and gets an 84 on their test, how many hours do they need to study to get a 100 on their test?

Answer: To find how many hours they need to study to get a 100 on their test, we can use the formula y = kx and plug in the given values:

y = kx
84 = k(6)
84/6 = k
14 = k
y = kx
100 = 14x
100/14 = x
7.14 x


So, they need to study about 7.14 hours to get a 100 on their test.

The cost of buying apples varies directly with the number of pounds bought. If it costs $3 to buy 2 pounds of apples, how much does it cost to buy 5 pounds of apples?

Answer: To find how much it costs to buy 5 pounds of apples, we can use the formula y = kx and plug in the given values:

y = kx
3 = k(2)
3/2 = k
1.5 = k
y = kx
y = 1.5(5)
y = 7.5


So, it costs $7.5 to buy 5 pounds of apples.

The distance traveled by a bike varies directly with the time spent riding. If a bike travels 60 miles in 4 hours, how far will it travel in 6 hours?

Answer: To find how far it will travel in 6 hours, we can use the formula y = kx and plug in the given values:

y = kx
60 = k(4)
60/4 = k
15 = k
y = kx
y = 15(6)
y = 90


So, it will travel 90 miles in 6 hours.

The number of words a person can type varies directly with the number of minutes they spend typing. If a person can type 300 words in 10 minutes, how many words can they type in 15 minutes?

Answer: To find how many words they can type in 15 minutes, we can use the formula y = kx and plug in the given values:

y = kx
300 = k(10)
300/10= k
30= k
y= kx
y=30(15)
y=450


So, they can type 450 words in 15 minutes.


We hope this article helped you understand direct variation and how to solve problems involving it. If you need more help with algebra or other math topics, check out our website for more resources and tips.



How to Check Your Answers for Direct Variation Problems?
After you solve a direct variation problem, you should always check your answer to make sure it is correct and reasonable. To check your answer, you can use one of these methods:



Plug your answer back into the original equation and see if it makes sense. For example, if you found that y = 50 when x = 10 using the equation y = kx, you can plug in y = 50 and x = 10 into the equation and see if it is true:

y = kx
50 = k(10)
50/10 = k
5 = k


This is the same value of k that we found before, so our answer is correct.

Use another pair of values for x and y that satisfy the direct variation and see if they match your answer. For example, if you found that y = 50 when x = 10 using the equation y = kx, you can use another pair of values, such as x = 5 and y = 25, and see if they match your answer:

y = kx
25 = k(5)
25/5 = k
5 = k


This is the same value of k that we found before, so our answer is correct.

Use a graphing calculator or an online graphing tool to graph the direct variation equation and see if it matches your answer. For example, if you found that y = 50 when x = 10 using the equation y = kx, you can graph the equation y = 5x and see if it passes through the point (10,50):



The graph shows that the line y = 5x passes through the point (10,50), so our answer is correct.

Lesson 5 Homework Practice Direct Variation Answer Key
Now that you know how to work with direct variation and how to check your answers, you can try some more homework practice problems. Here are some questions from lesson 5 homework practice direct variation worksheet, along with their answers and explanations.




If y varies directly with x and y = -12 when x = -6, determine x when y = -36.

Answer: To find x when y = -36, we can use the formula y = kx and plug in the given values:

y = kx
-12 = k(-6)
-12/-6 = k
2 = k
y = kx
-36 = 2x
-36/2 = x
-18 = x


So, x = -18 when y = -36.

The number of hours a person sleeps varies directly with the number of hours they are awake. If a person sleeps 6 hours when they are awake for 18 hours, how many hours do they sleep when they are awake for 24 hours?

Answer: To find how many hours they sleep when they are awake for 24 hours, we can use the formula y = kx and plug in the given values:

y = kx
6 = k(18)
6/18= k
0.33= k
y= kx
y=0.33(24)
y=7.92


So, they sleep about 7.92 hours when they are awake for 24 hours.

The cost of renting a bike varies directly with the number of hours rented. If it costs $9 to rent a bike for 3 hours, how much does it cost to rent a bike for 4 hours?

Answer: To find how much it costs to rent a bike for 4 hours, we can use the formula y = kx and plug in the given values:

y=kx
9=k(3)
9/3=k
3=k
y=kx
y=3(4)
y=12


So, it costs $12 to rent a bike for 4 hours.

The distance traveled by a plane varies directly with the time spent flying. If a plane travels 900 miles in 3 hours, how far will it travel in 5 hours?

Answer: To find how far it will travel in 5 hours, we can use the formula y=kx and plug in the given values:

y=kx
900=k(3)
900/3=k
300=k
y=kx
y=300(5)
y=1500


So,it will travel1500milesin5hours.

The number of words a person can read varies directly with their reading speed. If a person can read 240 words in one minute with a reading speed of 240 words per minute, how many words can they read in one minute with a reading speed of 300 words per minute?

Answer: To find how many words they can read in one minute with a reading speed of 300 words per minute, we can use the formula y=kx and plug in the given values:

y=kx
240=k(240)
240/240=k
1=k
y=kx
y=1(300)
y=300


So,the person can read300wordsin one minutewith a reading speedof300words per minute.


We hope this article helped you understand direct variation and how to check your answers.If you need more help with algebra or other math topicscheck out our websitefor more resourcesand tips.



Conclusion
In this article, we have learned what direct variation is, how to identify it, how to write an equation for it, how to use it to find missing values, how to apply it to real-world problems, and how to check our answers. We have also provided you with a lesson 5 homework practice direct variation answer key, so you can practice your skills and improve your understanding. Direct variation is a useful concept that can help you model and solve many situations that involve a proportional relationship between two variables. We hope you have enjoyed this article and found it helpful. If you have any questions or feedback, please let us know in the comments below. Thank you for reading and happy learning!

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