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 $45 \mathrm{~cm}$.
$\mathrm{cm}$

Question

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 $45 \mathrm{~cm}$.
$\mathrm{cm}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine which linear equation best describes the model, we need to consider the slope and y-intercept that would most likely match the data points and the line of best fit shown in the scatter plot. ‖ ‖ 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 $\hat{y}$.⚹◊What is the formula to calculate the slope of a line of best fit in a scatter plot⍭ Generate me a similar question◊

Sia