Question

Use the table to answer the question.

x (Hitting Attempts) f(x)=
(Kills)
21 11
13 6
18 9
16 9
24 11
22 12
Ava is a middle hitter on her club volleyball team. The table displays the number of hitting attempts she had in the last six games compared to the number of kills, which is when a hitting attempt hits the ground and scores a point. If the slope for the line of best fit is 12
, interpret the following representations of the slope and identify which statement is accurate.

(1 point)
Responses

Ava’s number of kills increases by 2 for every game.
Ava’s number of kills increases by 2 for every game.

Ava has about 2 kills for every hitting attempt.
Ava has about 2 kills for every hitting attempt.

Ava has about 1 kill for every 2 hitting attempts.
Ava has about 1 kill for every 2 hitting attempts.

Ava has about 2 kills for every game.
Ava has about 2 kills for every game.
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1 answer

To interpret the slope of the line of best fit, which is given as 12, we need to define what this slope represents in the context of the data provided.

Here, the slope (m) of 12 indicates that for each additional hitting attempt (x), the number of kills (f(x)) increases by 12. In other words, as Ava makes more hitting attempts in a game, we expect her number of kills to increase correspondingly.

Now, let's evaluate the available statements:

  1. Ava’s number of kills increases by 2 for every game.

    • This statement does not match with the slope of 12; it should refer to the number of hitting attempts.
  2. Ava has about 2 kills for every hitting attempt.

    • This does not correlate with a slope of 12; the slope refers to the rate of increase, not a ratio of kills to attempts.
  3. Ava has about 1 kill for every 2 hitting attempts.

    • This statement implies a 50% success rate for kills, which also does not relate to a slope of 12.
  4. Ava has about 2 kills for every game.

    • This does not reflect the slope either, as it does not discuss the relationship between hitting attempts and kills.

Given that no statement accurately reflects an increase of 12 kills for every additional hitting attempt, none of the provided options seem to correctly represent the slope of 12 expressed in clear terms.

However, if we take "kills" to understand that the interpretation should be that for every additional hitting attempt, the kills would increase significantly, thus if we were to summarize the increase more accurately in other terms, we'd clarify the meaning we looked for originally which was 'for each hitting attempt' leading towards a miscommunication in this instance.

Nonetheless, given the slope represents an increase, none of the options are exact but be mindful of how slope can interpret with various ratios in actual versus conceptual learnings.

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