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Exercises 1.[Finding the constant of proportionality] (Choose the correct answer for each question below.) (1) Let y be inversely proportional to x. When x=2, y=6, find the constant of proportionality. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=2 and y=6 into y=. 6= k=12 |
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(2) Let y be inversely proportional to x. When x=3, y=−6, find the constant of proportionality. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=3 and y=−6 into y=. −6= k=−18 |
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(3) Let y be inversely proportional to x. When x=−3, y=−, find the constant of proportionality. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=−3 and y=− into y=. −= k= |
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2.[Finding the value of y] (Choose the correct answer for each question below.) (1) Let y be inversely proportional to x. The value of y that corresponds to the value of x=3 is equal to −6. Find the value of y corresponding to the value of x=2. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=3 and y=−6 into y=. −6= k=−18 Substitute x=2 into y=−. y=−9 |
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(2) Let y be inversely proportional to x. The value of y that corresponds to the value of x=−2 is equal to 12. Find the value of y corresponding to the value of x=3. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=−2 and y=12 into y=. 12= k=−24 Substitute x=3 into y=−. y=−8 |
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(3) Let y be inversely proportional to x. The value of y that corresponds to the value of x=2 is equal to −6. Find the value of y corresponding to the value of x=−3. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=2 and y=−6 into y=. −6= k=−12 Substitute x=−3 into y=−. y=4 |
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3.[Finding the relationship] (Choose the correct answer for each question below.) (1) Let y be inversely proportional to x. The value of y that corresponds to the value of x=1 is equal to −3. Find the relationship between x and y. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=1 and y=−3 into y=. −3= k=−3 Therefore y==− |
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(2) Let y be inversely proportional to x. The value of y that corresponds to the value of x=−2 is equal to 6. Find the relationship between x and y. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=−2 and y=6 into y=. 6= k=−12 Therefore y==− |
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(3) Let y be inversely proportional to x. The value of y that corresponds to the value of x=−3 is equal to −2. Find the relationship between x and y. |
As y is inversely proportional to x, you can write y= where k is the constant of proportionality. Substitute x=−3 and y=−2 into y=. −2= k=6 Therefore y= |