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. Ther 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 1/2, intercept the following representations of the slope and identify which statement is accurate.

1 answer

To analyze the given information about Ava's hitting attempts and corresponding kills, first, let's understand what the slope of the line of best fit means in this context.

The slope \( m \) of a line represents the rate of change. In this case, the slope of \( \frac{1}{2} \) indicates that for every hitting attempt (x), Ava averages \(\frac{1}{2}\) of a kill. This means that for every 2 hitting attempts, Ava is expected to get 1 kill.

Next, let's represent this slope using the following definitions:

  1. Slope Representation: The slope can be represented as the ratio of change in kills to change in hitting attempts. Mathematically, if we consider two points on the line:

    \[ \text{slope} = \frac{\Delta f(x)}{\Delta x} = \frac{\text{change in kills}}{\text{change in hitting attempts}} = \frac{1}{2} \]

    This means that if she increases her hitting attempts by 2, her number of kills increases by 1.

  2. Intercept Representation: The y-intercept (not provided in your question) is the expected value of kills when the number of attempts (x) is zero.

Now let's analyze the statements:

To find the accuracy of specific statements:

  • If a statement claims that for every 2 hitting attempts, Ava makes 1 kill, then it is accurate because that matches the slope of \(\frac{1}{2}\).
  • If it states that as hitting attempts increase, the kills also increase, this is also true based on the positive slope.

Examples of accurate statements:

  • "For every 2 hitting attempts, Ava scores approximately 1 kill."
  • "If Ava has 0 hitting attempts, the expected number of kills would be the y-intercept."

If you have specific statements in mind that need to be evaluated for accuracy, please provide them so I can help you assess which one is accurate based on the slope of \(\frac{1}{2}\).