Final answer:
Noa's altitude increased at a rate of 740 meters per hour. After factoring in her initial position, the completed equation for the altitude (A) in relation to hours (h) driven is A = 740h - 400. Her initial altitude is considered to be -400 meters below sea level (Dead Sea elevation).
Step-by-step explanation:
Noa drove from the Dead Sea up to Jerusalem, and her altitude increased at a constant rate. After 1.5 hours of driving, her altitude was 710 meters above sea level.
To complete the equation for the relationship between altitude (A) in meters and the number of hours (h), we use the formula for a linear relationship: A = mt + b, where m is the rate of change, and b is the starting value or y-intercept.
Since Noa's altitude increased at a constant rate of 740 meters per hour, the rate of change (m) is 740. When she started driving from the Dead Sea, the lowest point on land, her altitude was approximately -430 meters below sea level (this is a known fact).
This initial altitude would be our b, the y-intercept. Since she ends up at 710 meters above sea level after 1.5 hours, we can use these values to find the y-intercept.
By substituting the given values into the equation A = mt + b, we get:
710 = 740(1.5) + b
710 = 1110 + b
b = 710 - 1110
b = -400
The complete equation for the relationship between the altitude and number of hours is therefore:
A = 740h - 400
This equation implies that for every hour Noa drives, her altitude increases by 740 meters, starting from -400 meters below sea level.