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. $\newline$ Let $y$ represent Noa's altitude (in meters) relative to sea level after $x$ hours. $\newline$ Complete the equation for the relationship between the altitude and number of hours.

View step-by-step help

Home

Math Problems

Grade 8

Interpreting Linear Expressions

Full solution

Q. 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.

\newline

Let

y

represent Noa's altitude (in meters) relative to sea level after

x

hours.

\newline

Complete the equation for the relationship between the altitude and number of hours.

Identify Rate of Change: Identify the rate of change in altitude and the initial condition. $\newline$ 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. $\newline$ 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. $\newline$ Initial altitude $=$ Final altitude $-$ (Rate of change $\times$ Time) $\newline$ Initial altitude $= 710$ meters $-$ ( $740$ meters/hour $\times 1.5$ hours) $\newline$ Initial altitude $= 710$ meters $-$ $710$ $1$ meters $\newline$ Initial altitude $710$ $2$ meters $\newline$ This means Noa started at $710$ $3$ 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. $\newline$ 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). $\newline$ 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). $\newline$ Therefore, the equation is $y = 740x - 400$ .