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?

choose 1 answer:
(a) \\(\hat{y} = x + 0.25\\)
(b) \\(\hat{y} = x + 0.5\\)

Explanation:

Identify the y-intercept of the line

The line intersects the vertical axis (Weight lost, \(y\)) at \(0.25\).

$$ y\text{-intercept} = 0.25 $$

Determine the slope of the line

Using the points \((0, 0.25)\) and \((4, 4.25)\) on the line:

$$ m = \frac{4.25 - 0.25}{4 - 0} = \frac{4}{4} = 1 $$

Formulate the linear equation

Combining the slope and y-intercept into the slope-intercept form:

$$ \hat{y} = 1x + 0.25 \implies \hat{y} = x + 0.25 $$

Answer:

• (A) \(\hat{y} = x + 0.25\) (Correct answer)
• (B) \(\hat{y} = x + 0.5\)