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 noas altitude (in meters) relative to sea level after x hours. complete the equation for the relationship between the altitude and number of hours.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). In this context, the rate of change of altitude (slope $m$) is 740 meters per hour, so $m = 740$.

Step2: Find the initial altitude ($b$)

We know that when $x = 1.5$ hours, $y = 710$ meters. Substitute these values and $m = 740$ into the equation $y=mx + b$:
\[710=740\times1.5 + b\]
First, calculate $740\times1.5$: $740\times1.5=1110$
Then, solve for $b$:
\[b=710 - 1110=- 400\]

Step3: Write the equation

Now that we know $m = 740$ and $b=-400$, the equation for the relationship between altitude $y$ and time $x$ (in hours) is $y = 740x-400$.

Answer:

\(y = 740x-400\)