Question

which of these linear equations best describes the given model?

choose 1 answer:
(a) \\(\hat{y} = 2x + 10\\)
(b) \\(\hat{y} = x + 10\\)
(c) \\(\hat{y} = 2x\\)
(d) \\(\hat{y} = x\\)

Explanation:

Identify the y-intercept of the line

The line of best fit passes directly through the origin \((0,0)\). Therefore, the y-intercept is:

$$ b = 0 $$

Calculate the slope of the line

Find two points on the line to estimate the slope:

$$ (0, 0) \quad \text{and} \quad (90, 90) $$

Calculate the slope \(m\):

$$ m = \frac{90 - 0}{90 - 0} = 1 $$

Determine the matching linear equation

Using the slope-intercept form \(\hat{y} = mx + b\):

$$ \hat{y} = 1x + 0 \implies \hat{y} = x $$

This corresponds to option (D).

Answer:

• (A) \(\hat{y} = 2x + 10\)
• (B) \(\hat{y} = x + 10\)

<mcq-option>(C) \(\hat{y} = 2x\)</mcq-correct>

• (D) \(\hat{y} = x\) (Correct answer)