a student has 20 pencils at the beginning of the school year. after a week, the student has 18 pencils left…

a student has 20 pencils at the beginning of the school year. after a week, the student has 18 pencils left. if the student continues to use pencils at the same rate, which equation will represent p pencils left after w weeks? p = -2w + 20 p = -2w - 20 p = 2w + 20 p = 2w - 20

a student has 20 pencils at the beginning of the school year. after a week, the student has 18 pencils left. if the student continues to use pencils at the same rate, which equation will represent p pencils left after w weeks? p = -2w + 20 p = -2w - 20 p = 2w + 20 p = 2w - 20

Answer

Explanation:

Step1: Calculate the rate of pencil usage

The student starts with 20 pencils ((p = 20) when (w = 0)). After 1 week ((w = 1)), (p=18). The change in the number of pencils per week (slope (m)) is (\frac{18 - 20}{1-0}=- 2).

Step2: Use the slope - intercept form (p=mw + b)

The slope - intercept form of a linear equation is (y = mx + b), where (m) is the slope and (b) is the (y) - intercept. Here, (m=-2) (rate of pencil usage) and (b = 20) (initial number of pencils). Substituting into (p=mw + b), we get (p=-2w + 20).

Answer:

(p=-2w + 20) (the first option)