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Use the table to answer the question.

x y
1 5
2 9
3 10
4 10.5
5 11
Use a spreadsheet calculator to determine the equation of the line of best fit for the data in this table. Round to the nearest hundredth, if needed.

(1 point)
Responses

y=x+5
y equals x plus 5

y=1.35x+5.05
y equals 1.35 x plus 5.05

y=5.05x+1.35
y equals 5.05 x plus 1.35

y=5x+11
y equals 5 x plus 11
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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 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’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 game.
Ava has about 2 kills for every game.
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Use the image to answer the question.

Four points are plotted on a coordinate plane, and a line is graphed through them. The x-axis is labeled Days and ranges from 0 to 600 in increments of 20. The y-axis is labeled Weight in Pounds and ranges from 250 to 2,500 in increments of 250.

An elephant calf is born weighing 282 pounds and gains about 2.5 pounds each day for its first year of life. After one year, the calf weighs approximately 1,195 pounds. The graph represents the line of best fit for the data. Which of the following interpretations of the slope is accurate?

(1 point)
Responses

The calf gains 737 pounds over 182 days.
The calf gains 737 pounds over 182 days.

The calf gains an average of 1,195 pounds over one year of life.
The calf gains an average of 1,195 pounds over one year of life.

The calf gains 365 pounds in 913 days.
The calf gains 365 pounds in 913 days.

The calf gains 5 pounds every 2 days.
The calf gains 5 pounds every 2 days.
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Use the linear model to make a prediction. The line of best fit y=0.37x+5
represents the tolls you pay after driving a specific number of miles. What prediction can be made based on this line of best fit?(1 point)
Responses

You can spend less than $30 to go 75 miles.
You can spend less than $30 to go 75 miles.

You can drive for 50 miles and spend less than $20.
You can drive for 50 miles and spend less than $20.

You can spend $42 to drive 100 miles.
You can spend $42 to drive 100 miles.

If you drove 10 miles, you would pay $42.
If you drove 10 miles, you would pay $42.

Linear Models Quick Check
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Question
Use the table to answer the question.

x
(Miles Run) y
(Weight in Pounds)
10 130
1 200
3 167
5 145
8 135
The weight of a cheetah can be based on the number of miles they run a day. The line of best fit for this dataset is y=195−7.3x
. The table represents the scatter plot of data. Find the weight of a cheetah that runs 7 miles, and state whether extrapolation or interpolation is occurring.

(1 point)
Responses

130 pounds and interpolation
130 pounds and interpolation

143.9 pounds and extrapolation
143.9 pounds and extrapolation

143.9 pounds and interpolation
143.9 pounds and interpolation

130 pounds and extrapolation
130 pounds and extrapolation
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1 answer

Let's break down each of the questions and find the correct answers based on the information provided.

  1. Finding the Line of Best Fit: For the first set of data in the table:

    x	y
1	5
2	9
3	10
4	10.5
5	11

    Using a spreadsheet calculator or a statistical software, the line of best fit (linear regression) can be calculated. After performing the regression analysis, the line of best fit is found to be approximately:

    y = 1.35x + 5.05.

    Therefore, the correct response here is:

    • y = 1.35x + 5.05

  2. Interpreting the Slope: For Ava's hitting attempts and kills data with a slope of 12:

    The slope of 12 indicates that for every additional hitting attempt, Ava is expected to get about 12 kills. But since we are not directly measuring hitting attempts but rather interpreting it, the approximate interpretation would be:

    • Ava has about 1 kill for every 2 hitting attempts. (since it's common to convey how many kills are to attempts in ratios).

    Note: you mentioned kills increases by 2, that context isn't correct as it suggests a smaller scale.

  3. Interpreting the Elephant Calf's Weight Gain: Given the information about the calf's weight gain of 2.5 pounds each day:

    Since the slope indicates the rate of gain:

    • The most accurate interpretation would be:
    • The calf gains 5 pounds every 2 days. (because 2.5 lbs/day × 2 days = 5 lbs)

  4. Using the Linear Model for Prediction: If the line of best fit is \( y = 0.37x + 5 \):

    We can make the following calculations based on the specified miles:

    • For 100 miles: \[ y = 0.37(100) + 5 = 37 + 5 = 42. \] Thus, the correct response is:
    • You can spend $42 to drive 100 miles.

  5. Finding the Weight of a Cheetah: The line of best fit is given as \( y = 195 - 7.3x \).

    To find the weight of a cheetah that runs 7 miles: \[ y = 195 - 7.3(7) = 195 - 51.1 = 143.9. \]

    Since 7 is within the range of provided data points (1 to 10), this is an interpolation.

    Therefore, the correct response here is:

    • 143.9 pounds and interpolation.

I hope this helps! Let me know if you need further assistance.