Question

question stella is going to drive from her house to city a without stopping. an equation that determines stellas distance from city a t hours after leaving her house is d = -60t + 240. what is the x - intercept of the equation and what is its interpretation in the context of the problem? answer attempt 1 out of 2 the x - intercept of the function is which represents

Explanation:

Step1: Recall x-intercept definition

The \( x \)-intercept (here \( t \)-intercept since \( t \) is the independent variable) occurs when \( D = 0 \). So set \( D = 0 \) in the equation \( D=-60t + 240 \).
\[
0=-60t + 240
\]

Step2: Solve for \( t \)

Add \( 60t \) to both sides:
\[
60t=240
\]
Divide both sides by 60:
\[
t=\frac{240}{60}=4
\]

Step3: Interpret the intercept

In the context, \( t \) is time in hours after leaving her house, and \( D \) is distance from City A. When \( D = 0 \), Stella is at City A. So the \( t \)-intercept (x-intercept here) \( t = 4 \) means Stella takes 4 hours to reach City A (or 4 hours after leaving her house, she is at City A, distance from City A is 0).

Answer:

The \( x \)-intercept ( \( t \)-intercept) is \( 4 \), which represents that Stella takes 4 hours to drive from her house to City A (or 4 hours after leaving her house, she arrives at City A, with a distance of 0 from City A).