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.

Question

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.

Bytelearn · Accepted Answer

Identify Rate of Change: Identify the rate of change in altitude and the initial condition. Noa's altitude increases at a constant rate of 740 meters per hour. Since she started at the Dead Sea, which is below sea level, we can assume her initial altitude is 0 meters. However, we need to consider that she ends up at 710 meters above sea level after 1.5 hours. This information will help us determine the initial altitude.Calculate Initial Altitude: Calculate the initial altitude using the information given. We know that after 1.5 hours, Noa's altitude is 710 meters. Using the rate of change, we can calculate the initial altitude (y-intercept) by subtracting the total change in altitude from the final altitude. Initial altitude = Final altitude - (Rate of change * Time) Initial altitude = 710 meters - (740 meters/hour * 1.5 hours) Initial altitude = 710 meters - 1110 meters Initial altitude = -400 meters This means Noa started at -400 meters relative to sea level, which is consistent with the Dead Sea's altitude.Write Equation: Write the equation using the rate of change and the initial altitude. The general form of the equation for a linear relationship is y = mx + b, where m is the rate of change (slope), and b is the initial value (y-intercept). In this context, y represents Noa's altitude after x hours, m is the rate of altitude increase per hour (740 meters/hour), and b is the initial altitude (-400 meters). Therefore, the equation is y = 740x - 400.

Full solution

More problems from Interpreting Linear Expressions

Related topics