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A large fish tank is having its water drained while being weighed. After 20 gallons have been drained, the tank weighs 1,909 pounds. After 50 gallons have been drained, it weighs 1,660 pounds. Let w be the weight of the tank and let g be the number of gallons drained. Write a linear equation for w in the terms of g.

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boffeemadrid

Answer:

[tex]w=-8.3g+2075[/tex]

Step-by-step explanation:

Let the x axis represent the gallons g

and y axis represent the weight of the tank w.

So, the first point on the plane will be [tex](20,1909)[/tex]

and the second point will be [tex](50,1660)[/tex]

The line between these points will be

[tex]w-1909=\dfrac{1660-1909}{50-20}(g-20)\\\Rightarrow w-1909=-\dfrac{249}{30}(g-20)\\\Rightarrow w-1909=-\dfrac{83}{10}(g-20)\\\Rightarrow w=-\dfrac{83}{10}g+\dfrac{83}{10}\times 20+1909\\\Rightarrow w=-\dfrac{83}{10}g+2075\\\Rightarrow w=-8.3g+2075[/tex]

The relationship between the weight and gallons of the tank is [tex]w=-8.3g+2075[/tex]

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