Question

a company produces items in small batches. the machinery needs to warm up before the items can be produced. the scatterplot shows the time needed to produce batches of different numbers of items.based on the line of best fit, which of these statements is true?a. each item requires about 3 minutes of production time.b. each item requires about 12 minutes of production time.c. the equipment starts producing items after about 25 minutes of warming up.d. the equipment starts producing items after about 20 minutes of warming up.

Explanation:

Step1: Find line equation form

The line of best fit follows $y = mx + b$, where $m$ is the slope (time per item) and $b$ is the y-intercept (warm-up time, when $x=0$).

Step2: Calculate slope $m$

Use points $(3, 44)$ and $(5, 60)$:
$$m = \frac{60 - 44}{5 - 3} = \frac{16}{2} = 8$$

Step3: Find y-intercept $b$

Substitute $x=3$, $y=44$, $m=8$ into $y=mx+b$:
$$44 = 8(3) + b$$
$$44 = 24 + b$$
$$b = 44 - 24 = 20$$

Step4: Evaluate each option

• A: Slope is 8, not 3 → False.
• B: Slope is 8, not 12 → False.
• C: Y-intercept is 20, not 25 → False.
• D: Y-intercept is 20, matching warm-up time → True.

Answer:

D. The equipment starts producing items after about 20 minutes of warming up.