Question

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 nour’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 =

Explanation:

Step1: Determine the slope (rate of change)

The initial altitude \( y_1 = -400 \) meters (400 meters below sea level) at \( x_1 = 0 \) hours. The final altitude \( y_2 = 1000 \) meters at \( x_2 = 2 \) hours. The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1000 - (-400)}{2 - 0}=\frac{1400}{2}=700 \).

Step2: Determine the y - intercept

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). When \( x = 0 \), \( y=-400 \), so \( b=-400 \).

Step3: Write the equation

Using the slope - intercept form of a linear equation \( y=mx + b \), with \( m = 700 \) and \( b=-400 \), we get \( y = 700x-400 \).

Answer:

\( y = 700x - 400 \)