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Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after 1.5 hours of driving, her altitude was 710 meters above sea level. Her altitude increased at a constant rate of 740 meters per hour. Let y represent Noa's altitude (in meters) relative to sea level after x hours. Complete the equation for the relationship between the altitude and number of hours. y=◻

Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after 11.55 hours of driving, her altitude was 710710 meters above sea level. Her altitude increased at a constant rate of 740740 meters per hour.\newlineLet y y represent Noa's altitude (in meters) relative to sea level after x x hours.\newlineComplete the equation for the relationship between the altitude and number of hours.\newliney=□ y=\square

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Q. Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after 11.55 hours of driving, her altitude was 710710 meters above sea level. Her altitude increased at a constant rate of 740740 meters per hour.\newlineLet y y represent Noa's altitude (in meters) relative to sea level after x x hours.\newlineComplete the equation for the relationship between the altitude and number of hours.\newliney=□ y=\square
  1. Identify Rate and Initial Altitude: Identify the rate of altitude change and the initial altitude.\newlineNoa's altitude increases at a constant rate of 740740 meters per hour. The initial altitude at the Dead Sea is not given, but we know that the Dead Sea is below sea level. However, we are only given the altitude after 1.51.5 hours of driving, which is 710710 meters above sea level. We will use this information to determine the initial altitude.
  2. Calculate Initial Altitude: Calculate the initial altitude when Noa started driving.\newlineSince Noa's altitude increased by 740 meters/hour740 \, \text{meters/hour} and she drove for 1.5 hours1.5 \, \text{hours}, we can calculate the altitude increase: 740 meters/hour×1.5 hours=1110 meters740 \, \text{meters/hour} \times 1.5 \, \text{hours} = 1110 \, \text{meters}. Since she ended up at 710 meters710 \, \text{meters} above sea level, we subtract the altitude increase from her final altitude to find the initial altitude: 710 meters−1110 meters=−400 meters710 \, \text{meters} - 1110 \, \text{meters} = -400 \, \text{meters}. This means Noa started at −400 meters-400 \, \text{meters} relative to sea level.
  3. Write Altitude Function Equation: Write the equation for Noa's altitude as a function of time.\newlineWe know that Noa's altitude increases at a constant rate, so the relationship between altitude and time is linear. The general form of a linear equation is y=mx+by = mx + b, where mm is the slope (rate of change) and bb is the y-intercept (initial value). In this case, mm is the rate of altitude change (740740 meters/hour) and bb is the initial altitude (−400-400 meters). Therefore, the equation is y=740x−400y = 740x - 400.

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