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A lake near the Arctic Circle is covered by a $2$ -meter- thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After $3$ weeks, the sheet is only $1.25$ meters thick. Let $y$ represent the ice sheet's thickness (in meters) after $2$ weeks. Complete the equation for the relationship between the thickness and number of weeks. $y=$

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Write a linear function: word problems

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Q. A lake near the Arctic Circle is covered by a

2

-meter- thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After

3

weeks, the sheet is only

1.25

meters thick. Let

y

represent the ice sheet's thickness (in meters) after

2

weeks. Complete the equation for the relationship between the thickness and number of weeks.

y=

Calculate melting rate: Determine the rate of ice melting per week. $\newline$ The ice thickness decreases from $2$ meters to $1.25$ meters over $3$ weeks. $\newline$ Change in thickness = $2 - 1.25 = 0.75$ meters. $\newline$ Time = $3$ weeks. $\newline$ Rate of melting = Change in thickness / Time = $0.75$ meters / $3$ weeks = $0.25$ meters per week.
Write thickness equation: Write the equation for the thickness of the ice sheet after $x$ weeks. $\newline$ Initial thickness = $2$ meters. $\newline$ Decrease per week = $0.25$ meters. $\newline$ Thickness after $x$ weeks = Initial thickness - (Decrease per week $*$ $x$ ). $\newline$ $y = 2 - 0.25x$ .
Find thickness after $2$ weeks: Substitute $x = 2$ into the equation to find the thickness after $2$ weeks. $y = 2 - 0.25 \times 2 = 2 - 0.5 = 1.5$ meters.

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