Answer :
Sure! Let's break down the problem and find the equation step by step.
1. Initial Water Level:
- On January 1st, the initial water level of Lake Conroe is measured at 195 feet. This means that when [tex]\( x = 0 \)[/tex] (the number of days since January 1st), the water level [tex]\( y \)[/tex] is 195 feet.
2. Daily Rate of Water Level Change:
- The water level is receding, meaning it is decreasing, at a rate of 1.5 feet per day.
3. Formulating the Equation:
- To find the water level [tex]\( y \)[/tex] on any given day [tex]\( x \)[/tex], we need to account for the reduction of the water level from the initial level. We start with 195 feet (the initial water level) and subtract the amount of water lost over [tex]\( x \)[/tex] days.
- Each day [tex]\( x \)[/tex], the water level drops by 1.5 feet. So in [tex]\( x \)[/tex] days, it drops [tex]\( 1.5 \times x \)[/tex] feet.
Therefore, the equation that relates the water level [tex]\( y \)[/tex] to the number of days [tex]\( x \)[/tex] since January 1st is:
[tex]\[
y = 195 - 1.5x
\][/tex]
4. Validating the Answer:
- Now we need to check which of the given options matches this equation. The options are:
- [tex]\( y = 1.5x - 195 \)[/tex]
- [tex]\( y = 195 + 1.5x \)[/tex]
- [tex]\( y = -1.5x - 195 \)[/tex]
- [tex]\( y = 195 - 1.5x \)[/tex]
- The correct equation we derived is [tex]\( y = 195 - 1.5x \)[/tex].
So, the correct answer is:
[tex]\[
y = 195 - 1.5x
\][/tex]
1. Initial Water Level:
- On January 1st, the initial water level of Lake Conroe is measured at 195 feet. This means that when [tex]\( x = 0 \)[/tex] (the number of days since January 1st), the water level [tex]\( y \)[/tex] is 195 feet.
2. Daily Rate of Water Level Change:
- The water level is receding, meaning it is decreasing, at a rate of 1.5 feet per day.
3. Formulating the Equation:
- To find the water level [tex]\( y \)[/tex] on any given day [tex]\( x \)[/tex], we need to account for the reduction of the water level from the initial level. We start with 195 feet (the initial water level) and subtract the amount of water lost over [tex]\( x \)[/tex] days.
- Each day [tex]\( x \)[/tex], the water level drops by 1.5 feet. So in [tex]\( x \)[/tex] days, it drops [tex]\( 1.5 \times x \)[/tex] feet.
Therefore, the equation that relates the water level [tex]\( y \)[/tex] to the number of days [tex]\( x \)[/tex] since January 1st is:
[tex]\[
y = 195 - 1.5x
\][/tex]
4. Validating the Answer:
- Now we need to check which of the given options matches this equation. The options are:
- [tex]\( y = 1.5x - 195 \)[/tex]
- [tex]\( y = 195 + 1.5x \)[/tex]
- [tex]\( y = -1.5x - 195 \)[/tex]
- [tex]\( y = 195 - 1.5x \)[/tex]
- The correct equation we derived is [tex]\( y = 195 - 1.5x \)[/tex].
So, the correct answer is:
[tex]\[
y = 195 - 1.5x
\][/tex]
