baruti, a ranger in kruger national park in south africa, collected data about the elephant population in…

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: $hat{y}=6x - 20$, $hat{y}=6x + 20$, $hat{y}=\frac{3}{2}x - 20$, $hat{y}=\frac{3}{2}x + 20$. based on this equation, estimate the shoulder height for an elephant whose foot length is 45 cm.

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: $hat{y}=6x - 20$, $hat{y}=6x + 20$, $hat{y}=\frac{3}{2}x - 20$, $hat{y}=\frac{3}{2}x + 20$. based on this equation, estimate the shoulder height for an elephant whose foot length is 45 cm.

Answer

Explanation:

Step1: Find the y - intercept

The line intersects the y - axis above the origin. When (x = 0), (y>0). In the slope - intercept form (y=mx + b) ((m) is the slope and (b) is the y - intercept), the y - intercept (b>0). This rules out options A and C which have (b=- 20).

Step2: Estimate the slope

Pick two points on the line, say ((10,80)) and ((20,140)). The slope (m=\frac{\Delta y}{\Delta x}=\frac{140 - 80}{20 - 10}=\frac{60}{10}=6). So the equation of the line is (y = 6x+20), and the best - fitting linear equation is option B.

Step3: Estimate the shoulder height

We use the equation (y = 6x+20) from step 2. Substitute (x = 45) into the equation. [ \begin{align*} y&=6\times45+20\ &=270 + 20\ &=290 \end{align*} ]

Answer:

B. (\hat{y}=6x + 20) 290