Question

The cheetah is the fastest land animal in the world. During a sprint, the number of feet a cheetah runs y varies directly with the amount of time in seconds x as shown in the table. Write and solve a direct variation equation to determine how far the cheetah can run in 5.5 seconds.

Answer 1

Step-by-step explanation:

`\hookrightarrow \sf y = kx`

`\sf where \: k \: is \: constant`

`\sf \: k = (y)/(x)`

`\hookrightarrow \sf \: k = (y)/(5.5)`

Equation =
`\sf \: k = (y)/(5.5)`

Answer 2

The cheetah can run approximately 539 feet in 5.5 seconds based on direct variation.

Step-by-step explanation:

In a direct variation equation, the relationship between two variables, x and y, is expressed as:

y = kx

Where k is the constant of variation.

To find the constant of variation (k), we can use any of the given data points. Let's use the point (3.5, 343):

y = kx

343 = k × 3.5

`k = (343)/(3.5)`

k ≈ 98

Now that we have the constant of variation (k ≈ 98), we can use this to determine the distance the cheetah can run in 5.5 seconds:

y = kx

y = 98 × 5.5

y ≈ 539

Therefore, the cheetah can run approximately 539 feet in 5.5 seconds based on the direct variation relationship established from the given data.