Question

the linear function f computes the distance y in miles between a car and a city after x hours, where $0 \leq x \leq 10$. the graphs of f and the horizontal lines $y = 200$ and $y = 300$ are shown. use the graph to answer the following.1. is the car moving toward or away from the city?$quad$ away$quad$ toward2. determine the time when the car is 300 miles from the city.

Explanation:

Step1: Analyze direction of movement

As time $x$ increases, the distance $y=f(x)$ increases from 100 miles to over 400 miles. This means the car's distance from the city is growing, so it is moving away.

Step2: Find equation of $y=f(x)$

The line passes through $(0, 100)$ and $(10, 500)$. Calculate slope:
$\text{slope} = \frac{500-100}{10-0} = 40$
Using slope-intercept form $y=mx+b$ with $b=100$, the equation is $y=40x+100$.

Step3: Solve for $x$ when $y=300$

Substitute $y=300$ into the equation:
$300 = 40x + 100$
Subtract 100 from both sides:
$300 - 100 = 40x$
$200 = 40x$
Divide by 40:
$x = \frac{200}{40} = 5$

Answer:

1. The car is moving Away from the city.
2. 5 hours