Question

Aubrey and Charlie are driving to a city that is 120 miles from their house. they have already traveled 20 miles ,and they are driving at a constant rate of 50 mi /h. write a function that models the distance they drive as a function of time .what is a reasonable domain for this situation ?

Answer 1

Answer:

The linear function is $y=50x+20$

The reasonable domain is $0\ hours \leq x\leq 2\ hours$

Step-by-step explanation:

Let

x ----> the time in hours

y ---> the distance in miles

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

The slope is $m=50\ \frac{miles}{hour}$

The y-intercept is $b=20\ miles$

substitute

$y=50x+20$

Find the domain for x

For y=120 miles

Find the value of x

substitute the value of y in the linear equation and solve for x

$120=50x+20$

$50x=120-20$

$50x=100$

$x=2\ hours$

therefore

The domain is the interval [0,2]

$0\ hours \leq x\leq 2\ hours$