Question

janell has 5 gallons of paint. after painting 800 square feet of walls in her house, she has 3 gallons left. the graph below show’s janell’s situation. janell has 5 gallons of paint. after painting 800 square feet of walls in her house, she has 3 gallons left. the graph below show’s janell’s situation. what is the equation of this linear function? what is the slope and what does it represent? a. $y = -\frac{1}{400}x + 5$; slope $= -\frac{1}{400}$; this means that for every gallon of paint used, 400 sq. ft. of area is painted. b. $y = -\frac{1}{40}x + 5$; slope $= -\frac{1}{40}$; this means that for every gallon of paint used, 40 sq. ft. of area is painted. c. $y = -\frac{1}{800}x + 5$; slope $= -\frac{1}{800}$; this means that for every gallon of paint used, 800 sq. ft. of area is painted. d. $y = -\frac{1}{4}x + 5$; slope $= -\frac{1}{400}$; this means that for every gallon of paint used, 4 sq. ft. of area is painted. a b c d

Explanation:

Step1: Identify points

Initial point: (0,5) (0 sq ft painted, 5 gallons left). After 800 sq ft, 3 gallons left: (800,3).

Step2: Calculate slope

Slope $m=\frac{3-5}{800-0}=-\frac{2}{800}=-\frac{1}{400}$.

Step3: Find equation

Using $y=mx+b$, $b=5$, so $y=-\frac{1}{400}x+5$.

Step4: Interpret slope

Slope $-\frac{1}{400}$ means $\frac{\Delta y}{\Delta x}=-\frac{1}{400}$ → $\Delta x=-400\Delta y$. When 1 gallon is used ($\Delta y=-1$), $\Delta x=400$ sq ft painted.

Answer:

A. $y=-\frac{1}{400}x + 5$; slope = $-\frac{1}{400}$; this means that for every gallon of paint used, 400 sq. ft. of area is painted.