Answer:
Step-by-step explanation:
xy = k
where k is the constant of variation.
We can also express the relationship between x and y as:
y =
where k is the constant of variation.
Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10. Thus, the equation describing this inverse variation is xy = 10 or y = .
Example 1: If y varies inversely as x, and y = 6 when x = , write an equation describing this inverse variation.
k = (6) = 8
xy = 8 or y =
Example 2: If y varies inversely as x, and the constant of variation is k = , what is y when x = 10?
xy =
10y =
y = × = × =
k is constant. Thus, given any two points (x1, y1) and (x2, y2) which satisfy the inverse variation, x1y1 = k and x2y2 = k. Consequently, x1y1 = x2y2 for any two points that satisfy the inverse variation.
Example 3: If y varies inversely as x, and y = 10 when x = 6, then what is y when x = 15?
x1y1 = x2y2
6(10) = 15y
60 = 15y
y = 4
Thus, when x = 6, y = 4.
2nd answer choice
constant of variation is xy. XY=23. If X=7 then Y=23/7.
<u>Answer:</u>
- 16 marbles.
- 15 balloons.
<u>Step-by-step explanation:</u>
<u>Question-1 solution:</u>
<u>We can solve this question with the help of proportion. Seek solution below!</u>
- 6:4 = 24:x
- => 6x = 96
- => x = 16
Hence, for question 1, the answer is 16 marbles.
<u>Question-2 solution:</u>
<u>We can solve this question with the help of proportion. Seek solution below!</u>
- 6:4 = x:10
- => 60 = 4x
- => x = 15
Hence, for question 2, the answer is 15 balloons.
Hoped this helped.
