find the equation of the line which satisfy the given condition: The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs. 14/litre and 1220 litres of milk each week at Rs. 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs. 17/litre?

Class 11 | Exercise 10.2 | Maths | NCERT | Straight Lines

find the equation of the line which satisfy the given condition: The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs. 14/litre and 1220 litres of milk each week at Rs. 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs. 17/litre?

Accepting the connection between selling cost and request is direct.

Allow us to accept selling cost per liter along X-pivot and request along Y-hub, we have two focuses \[\left( \mathbf{14},\text{ }\mathbf{980} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{16},\text{ }\mathbf{1220} \right)\] in XY-plane.

We realize that the condition of the line going through the focuses (x1, y1) and (x2, y2) is given by

\[\mathbf{y}\text{ }\text{ }\mathbf{-980}\text{ }=\text{ }\mathbf{120}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{-14} \right)\]

\[\mathbf{y}\text{ }=\text{ }\mathbf{120}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{-14} \right)\text{ }+\text{ }\mathbf{980}\]

At the point when \[\mathbf{x}\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{17}/\mathbf{liter},\]

\[\mathbf{y}\text{ }=\text{ }\mathbf{120}\text{ }\left( \mathbf{17}\text{ }\text{ }\mathbf{-14} \right)\text{ }+\text{ }\mathbf{980}\]

\[\mathbf{y}\text{ }=\text{ }\mathbf{120}\left( \mathbf{3} \right)\text{ }+\text{ }\mathbf{980}\]

\[\mathbf{y}\text{ }=\text{ }\mathbf{360}\text{ }+\text{ }\mathbf{980}\text{ }=\text{ }\mathbf{1340}\]

∴ The proprietor can sell 1340 liters week by week at \[\mathbf{Rs}.\text{ }\mathbf{17}/\mathbf{liter}.\]

i

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