Question

Arthur wanted to investigate how the amount he exercises impacts his weight loss. each week he recorded the number of hours he exercised and the amount of weight he lost that week (in kilograms). a line was fit to the data to model the relationship. Which of these linear equations best describes the given model?

A) \( y = 2x + 5 \)

B) \( y = 0.5x + 10 \)

C) \( y = 3x - 2 \)

D) \( y = -1.5x + 8 \)

Answer 1

Answer: y=0.5x+0.25 and the bottom answer is 6 hours

We need the slope and the

\[y\]-intercept to find the equation of the linear model.

This line goes through

\[(0.5,0.5)\] and

\[(1.5,1)\], so the slope is

\[\dfrac{1-0.5}{1.5-0.5} = 0.5\].

We can see that the line passes through

\[(0,0.25)\], so the

\[y\]-intercept is

\[0.25\].

The equation that best describes the model is

\[\hat y=0.5x+0.25\].

Hint #22 / 3

Using the line to make a prediction

To estimate Arthur's weight loss in a week where he exercises for

\[6\] hours, we can plug in

\[6\] for

\[x\] in the equation like this:

\[\begin{aligned}\hat y&=0.5x+0.25\\

\hat y&=\left(0.5\right)\left(6\right)+0.25\\

\hat y&=3+0.25\\

\hat y&=3.25\end{aligned}\]

Hint #33 / 3

The answers

The equation of the model shown is

\[\hat y=0.5x+0.25\].

Based on this equation, we estimate that Arther will lose

\[3.25\,\text{kg}\] in a week where he exercises for

\[6\] hours.

Explanation: The answer is y=0.5x+0.25 here's why.

Answer 2

Arthur's model on the correlation between exercise and weight loss is best described by options A, B, or C, as they all suggest an increase in exercise leads to an increase in weight loss, with the specific option depending on Arthur's data.

Step-by-step explanation:

To determine which linear equation best describes the model for Arthur’s exercise and weight loss data, we need to consider several key characteristics of the given options. Each equation is in the standard linear form y = mx + b, where y represents weight loss, x represents the number of hours exercised, m indicates the rate of weight loss per hour of exercise (slope), and b signifies the starting point or initial weight loss (y-intercept) without any exercise.

Options A) y = 2x + 5, B) y = 0.5x + 10, and C) y = 3x - 2 suggest that as Arthur exercises more (increases in x), his weight loss (y) also increases, which aligns with the general understanding that more exercise leads to more weight loss. However, option D) y = -1.5x + 8 implies that as the number of exercise hours goes up, the weight loss would decrease, which does not make sense in this context. Therefore, options A, B, or C are plausible, with the correct option depending on the actual data that Arthur collected.