Write an Equation for Hyperbolas

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Question 1 of 3

1. Question
Write the equation of the cubic graph shown on the number plane below.
- `y=\frac{8}{x}`
- `x=\frac{8}{y}`
- `y=\frac{x}{8}`
- `y=\frac{4}{x}`
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Correct

Excellent!

Incorrect

The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.

Use the point `(2,4)` shown on the graph to find the value of `k`.

The `x`-coordinate of this point is `2`, and the `y`-coordinate of this point is `4`.

So we should substitute `x=2` and `y=4` into the equation `y``x``=k`, and solve to find `k`.

`4``\cdot``2``=k`.

`k=8`

Substitute the value for `k` and write the equation of the graph.

`y=\frac{8}{x}`
Question 2 of 3

2. Question
Write the equation of the cubic graph shown on the number plane below.
- `y=\frac{-6}{x}`
- `y=\frac{6}{x}`
- `y=\frac{x}{-6}`
- `y=\frac{-2}{x}`
Hint

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Correct

Fantastic!

Incorrect

The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.

Use the point `(2,-3)` shown on the graph to find the value of `k`.

The `x`-coordinate of this point is `2`, and the `y`-coordinate of this point is `-3`.

So we should substitute `x=2` and `y=-3` into the equation `y``x``=k`, and solve to find `k`.

`-3``\cdot``2``=k`.

`k=-6`

Substitute the value for `k` and write the equation of the graph.

`y=\frac{-6}{x}`
Question 3 of 3

3. Question
Write the equation of the cubic graph shown on the number plane below.
- `y=\frac{-20}{x}`
- `y=\frac{20}{x}`
- `y=\frac{x}{8}`
- `y=\frac{-5}{x}`
Hint

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Correct

Exceptional!

Incorrect

The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.

Use the point `(5,-4)` shown on the graph to find the value of `k`.

The `x`-coordinate of this point is `5`, and the `y`-coordinate of this point is `-4`.

So we should substitute `x=5` and `y=-4` into the equation `y``x``=k`, and solve to find `k`.

`-4``\cdot``5``=k`.

`k=-20`

Substitute the value for `k` and write the equation of the graph.

`y=\frac{-20}{x}`

Write an Equation for Hyperbolas

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