Direct variation is a mathematical relationship where one quantity changes...
Algebra 131 views·Updated Jun 15, 2026·1 pageUnderstanding Direct Variation in Algebra 1
lori@vvlvvrs
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Direct Variation
Direct variation is written as the equation y = kx, where k is the constant of variation (or rate). This relationship means that when x doubles, y doubles too. When x is cut in half, y is cut in half as well.
Let's see how this works in real situations. When the Acela Express train travels 455 miles in 7 hours, we can find how far it goes in 4 hours by finding the constant k first. We divide 455 by 7 to get k = 65, meaning the train travels at 65 miles per hour. Then we multiply: y = 65(4) = 260 miles in 4 hours.
The same approach works for calculating pay. If Heather earns $174 for 24 hours of work, her rate is $7.25 per hour (found by dividing 174 by 24). So for 40 hours, she'll earn y = 7.25(40) = $290.
Quick Tip: To solve any direct variation problem, first find the constant k using a known pair of values, then use that k to find any unknown values.
For calorie burning, if a 150-pound person burns 207 calories swimming for 30 minutes, the rate is 6.9 calories per minute. To burn 520 calories, they need to swim for approximately 75.4 minutes (520 ÷ 6.9). Direct variation makes calculating these proportional relationships straightforward!
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Algebra 131 views·Updated Jun 15, 2026·1 pageUnderstanding Direct Variation in Algebra 1
lori@vvlvvrs
Direct variation is a mathematical relationship where one quantity changes in direct proportion to another. This means as one value increases or decreases, the other changes by the same factor. Understanding direct variation helps solve real-world problems involving rates, time,...
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Direct Variation
Direct variation is written as the equation y = kx, where k is the constant of variation (or rate). This relationship means that when x doubles, y doubles too. When x is cut in half, y is cut in half as well.
Let's see how this works in real situations. When the Acela Express train travels 455 miles in 7 hours, we can find how far it goes in 4 hours by finding the constant k first. We divide 455 by 7 to get k = 65, meaning the train travels at 65 miles per hour. Then we multiply: y = 65(4) = 260 miles in 4 hours.
The same approach works for calculating pay. If Heather earns $174 for 24 hours of work, her rate is $7.25 per hour (found by dividing 174 by 24). So for 40 hours, she'll earn y = 7.25(40) = $290.
Quick Tip: To solve any direct variation problem, first find the constant k using a known pair of values, then use that k to find any unknown values.
For calorie burning, if a 150-pound person burns 207 calories swimming for 30 minutes, the rate is 6.9 calories per minute. To burn 520 calories, they need to swim for approximately 75.4 minutes (520 ÷ 6.9). Direct variation makes calculating these proportional relationships straightforward!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Analyze the initial social and religious encounters between Europeans, Africans, and Indigenous peoples in the colonial Americas.
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Analyze the environmental factors and technological innovations that led to the rise of early states in Mesopotamia, Egypt, and the Indus Valley.
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Examine the diverse social, political, and economic structures of North American indigenous groups prior to European contact.
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