nour drove from the dead sea up to amman, and her altitude increased at a constant rate. when she began…

nour drove from the dead sea up to amman, and her altitude increased at a constant rate. when she began driving, her altitude was 400 meters below sea level. when she arrived in amman 2 hours later, her altitude was 1000 meters above sea level. let y represent nours altitude (in meters) relative to sea level after x hours. complete the equation for the relationship between the altitude and number of hours. y =

nour drove from the dead sea up to amman, and her altitude increased at a constant rate. when she began driving, her altitude was 400 meters below sea level. when she arrived in amman 2 hours later, her altitude was 1000 meters above sea level. let y represent nours altitude (in meters) relative to sea level after x hours. complete the equation for the relationship between the altitude and number of hours. y =

Answer

Explanation:

Step1: Calculate the total altitude change

The initial altitude is - 400 meters (below sea - level) and the final altitude is 1000 meters (above sea - level). The total change in altitude $\Delta y=1000-( - 400)=1400$ meters.

Step2: Calculate the rate of change

The time taken $\Delta x = 2$ hours. The rate of change (slope $m$) of altitude with respect to time is $m=\frac{\Delta y}{\Delta x}=\frac{1400}{2}=700$ meters per hour.

Step3: Determine the y - intercept

The initial condition is when $x = 0$, $y=-400$. In the slope - intercept form of a linear equation $y=mx + b$ (where $m$ is the slope and $b$ is the y - intercept), $b=-400$.

Step4: Write the equation

The equation for the relationship between altitude $y$ and number of hours $x$ is $y = 700x-400$.

Answer:

$y = 700x-400$