Question

Math

Posted 4 months ago

```
Baruti, a ranger in Kruger National Park in South Africa, collected data about the elephant population in the park. She compared the foot lengths of the elephants and their shoulder height (both in centimeters) and created the following scatter plot. A line was fit to the data to model the relationship.
Which of these linear equations best describes the given model?
Choose 1 answer:
(A) $\hat{y}=6 x-20$
(B) $\hat{y}=6 x+20$
(C) $\hat{y}=\frac{3}{2} x-20$
() $\hat{y}=\frac{3}{2} x+20$
Based on this equation, estimate the shoulder height for an elephant whose foot length is $45 \mathrm{~cm}$.
$\mathrm{cm}$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

The slope of the line should be positive, as the scatter plot shows a positive correlation between foot length and shoulder height

step 3

The y-intercept should be a value that the line would cross when x (foot length) is 0. We need to choose the equation with a y-intercept that makes sense in the context of the data

step 4

Based on the given options, the equation with a positive slope and a reasonable y-intercept that matches the context of the scatter plot is the correct choice

step 5

To estimate the shoulder height for an elephant whose foot length is 45 cm, we substitute x = 45 into the correct linear equation

step 6

After substituting x = 45, we calculate the value of $\hat{y}$, which will give us the estimated shoulder height in centimeters

1 Answer

C

Key Concept

Choosing the correct linear equation

Explanation

The correct linear equation is chosen by matching the slope and y-intercept to the data's trend and context.

Key Concept

Estimating values using the line of best fit

Explanation

To estimate a value using the line of best fit, substitute the given x-value into the equation and solve for $\hat{y}$.

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