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Direct & Inverse Proportions Class 8 PPT
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Page 1 Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such that Variation The number k is called the constant of variation or the constant of proportionality . kx y ? Verbal Phrase Expression ?? ???????? ???? ???????? ???????? ??????h ?? ?? = ???? ?? ???????? ???? ???????? ???????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ?????? ?? ???? ?? ?? = ?? ?? 3 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ???? . ???? . ???? ?? ?? = ?? ?? Page 2 Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such that Variation The number k is called the constant of variation or the constant of proportionality . kx y ? Verbal Phrase Expression ?? ???????? ???? ???????? ???????? ??????h ?? ?? = ???? ?? ???????? ???? ???????? ???????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ?????? ?? ???? ?? ?? = ?? ?? 3 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ???? . ???? . ???? ?? ?? = ?? ?? 1. y varies directly as x. 2. y is directly proportional to x. 3. y = kx for some nonzero constant m. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = kx yields 3 = m(2) or m = 1.5. Thus, y = 1.5x. Direct Variation Statements Page 3 Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such that Variation The number k is called the constant of variation or the constant of proportionality . kx y ? Verbal Phrase Expression ?? ???????? ???? ???????? ???????? ??????h ?? ?? = ???? ?? ???????? ???? ???????? ???????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ?????? ?? ???? ?? ?? = ?? ?? 3 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ???? . ???? . ???? ?? ?? = ?? ?? 1. y varies directly as x. 2. y is directly proportional to x. 3. y = kx for some nonzero constant m. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = kx yields 3 = m(2) or m = 1.5. Thus, y = 1.5x. Direct Variation Statements Direct Variation kx y ? ? ? 8 24 k ? k ? 8 24 Suppose y varies directly as x. If y is 24 when x is 8, find the constant of variation (k) and the direct variation equation. 3 ? k x y 3 ? direct variation equation constant of variation x y 3 9 5 15 9 27 13 39 Variation Page 4 Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such that Variation The number k is called the constant of variation or the constant of proportionality . kx y ? Verbal Phrase Expression ?? ???????? ???? ???????? ???????? ??????h ?? ?? = ???? ?? ???????? ???? ???????? ???????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ?????? ?? ???? ?? ?? = ?? ?? 3 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ???? . ???? . ???? ?? ?? = ?? ?? 1. y varies directly as x. 2. y is directly proportional to x. 3. y = kx for some nonzero constant m. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = kx yields 3 = m(2) or m = 1.5. Thus, y = 1.5x. Direct Variation Statements Direct Variation kx y ? ? ? 8 24 k ? k ? 8 24 Suppose y varies directly as x. If y is 24 when x is 8, find the constant of variation (k) and the direct variation equation. 3 ? k x y 3 ? direct variation equation constant of variation x y 3 9 5 15 9 27 13 39 Variation Inverse Variation: y varies inversely as x (y is inversely proportional to x), if there is a nonzero constant k such that The number k is called the constant of variation or the constant of proportionality. . x k y ? Verbal Phrase Expression ?? ???? ???????????? ?????? ?????????? ?????? ???????? ??????h ?? ?? = ?? ?? ?? ???????? ???? ???????????? ?????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????????? ?????? ?????????? ?????? ?????? ?? ???? ?? 4 ?? = ?? ?? 4 ?? ???????? ???? ???????????? ?????? ??????h ??h?? ???????? . ???? . ???? ?? ?? = ?? 3 ?? Variation Page 5 Direct Variation: y varies directly as x (y is directly proportional to x), if there is a nonzero constant k such that Variation The number k is called the constant of variation or the constant of proportionality . kx y ? Verbal Phrase Expression ?? ???????? ???? ???????? ???????? ??????h ?? ?? = ???? ?? ???????? ???? ???????? ???????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ?????? ?? ???? ?? ?? = ?? ?? 3 ?? ???? ???????? ???????? ???????? . ??????h ??h?? ???? . ???? . ???? ?? ?? = ?? ?? 1. y varies directly as x. 2. y is directly proportional to x. 3. y = kx for some nonzero constant m. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = kx yields 3 = m(2) or m = 1.5. Thus, y = 1.5x. Direct Variation Statements Direct Variation kx y ? ? ? 8 24 k ? k ? 8 24 Suppose y varies directly as x. If y is 24 when x is 8, find the constant of variation (k) and the direct variation equation. 3 ? k x y 3 ? direct variation equation constant of variation x y 3 9 5 15 9 27 13 39 Variation Inverse Variation: y varies inversely as x (y is inversely proportional to x), if there is a nonzero constant k such that The number k is called the constant of variation or the constant of proportionality. . x k y ? Verbal Phrase Expression ?? ???? ???????????? ?????? ?????????? ?????? ???????? ??????h ?? ?? = ?? ?? ?? ???????? ???? ???????????? ?????? ??????h ??h?? ?????????? ?? ???? ?? ?? = ?? ?? 2 ?? ???? ???????????? ?????? ?????????? ?????? ?????? ?? ???? ?? 4 ?? = ?? ?? 4 ?? ???????? ???? ???????????? ?????? ??????h ??h?? ???????? . ???? . ???? ?? ?? = ?? 3 ?? Variation 1. y varies inversely as x. 2. y is inversely proportional to x. 3. y = k / x for some nonzero constant k. NOTE: k is the constant of variation or the constant of proportionality. Example: If y = 3 when x = 2, find k. y = k / x yields 3 = k / 2 or k = 6. Thus, y = 6 / x. Inverse Variation StatementsRead More
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FAQs on Direct & Inverse Proportions Class 8 PPT
| 1. What is direct proportion? |  |
Ans. Direct proportion is a mathematical relationship between two variables where an increase or decrease in one variable results in a corresponding increase or decrease in the other variable. In simple terms, if one variable doubles, the other variable also doubles, and if one variable is halved, the other variable is also halved.
| 2. What is inverse proportion? | |
Ans. Inverse proportion is a mathematical relationship between two variables where an increase in one variable results in a corresponding decrease in the other variable, and vice versa. In this case, if one variable doubles, the other variable is halved, and if one variable is halved, the other variable doubles.
| 3. How can we identify direct proportion in a given problem? | |
Ans. To identify direct proportion in a given problem, we need to check if an increase or decrease in one variable directly affects the other variable in the same way. If both variables increase or decrease together, then they are in direct proportion. Additionally, if the ratio of the two variables remains constant, it indicates a direct proportion.
| 4. How can we identify inverse proportion in a given problem? | |
Ans. To identify inverse proportion in a given problem, we need to check if an increase in one variable leads to a decrease in the other variable, and vice versa. If the product of the two variables remains constant, it indicates an inverse proportion. Additionally, if the ratio of one variable to the other is constant, it also indicates an inverse proportion.
| 5. Can a relationship be both direct and inverse proportion at the same time? | |
Ans. No, a relationship cannot be both direct and inverse proportion at the same time. Direct proportion implies that as one variable increases, the other variable also increases, while inverse proportion implies that as one variable increases, the other variable decreases. These two concepts are opposite of each other and cannot coexist in a single relationship.
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Dec 22, 2024 Last updated |
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