Question

equals \\(\frac{90 - 100}{30 - 0} = \frac{-10}{30} = -\frac{1}{3}\\)\
what does the slope represent in this situation?\
the water quality score decreases by 3 points for every gallon of water processed.\
the water quality score decreases by 1 for every 3 gallons of water processed.\
the water quality score increases by 3 points for every gallon of water removed\
chart: bottle filter water quality test, x - axis: gallons of water processed, y - axis: water quality score, with data points showing a trend

Explanation:

The slope is calculated as $\frac{\text{Change in Water Quality Score}}{\text{Change in Gallons of Water Processed}}=\frac{90 - 100}{30 - 0}=-\frac{10}{30}=-\frac{1}{3}$. A negative slope means the water quality score decreases. The slope $-\frac{1}{3}$ implies that for every 3 gallons of water processed (change in x by 3), the water quality score decreases by 1 (change in y by - 1, since slope is $\frac{\Delta y}{\Delta x}=-\frac{1}{3}$, so $\Delta y =-\frac{1}{3}\times\Delta x$, when $\Delta x = 3$, $\Delta y=- 1$).

Answer:

The water quality score decreases by 1 for every 3 gallons of water processed.