Final answer:
The slope in the equation represents the rate at which the gas in the lawnmower tank decreases with each yard mowing, specifically a decrease of 2 gallons per mowing.
Step-by-step explanation:
The student is asking about the meaning of the slope in the equation y = -2x + 7, which models the amount of gas in the tank of a lawnmower as it is used to mow the entire yard multiple times. The slope in a linear equation like this one is represented by the letter m, and it indicates how much the y-value, or in this context, the amount of gas, decreases with each increase of one unit in the x-value, which here represents each complete mowing of the yard.
The slope of -2 in the equation means that each time the entire yard is mowed, the amount of gas in the tank decreases by 2 gallons. The negative sign indicates a decrease in the y-value as the x-value increases. This is consistent with the given information that the lawnmower uses 2 gallons of gas every time the yard is mowed. Therefore, the slope of the line graph that would represent this equation gives us the rate at which the gas in the tank decreases as the yard is mowed more times.