Answer:
The linear function is [tex]y=50x+20[/tex]
The reasonable domain is [tex]0\ hours \leq x\leq 2\ hours[/tex]
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
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
The slope is [tex]m=50\ \frac{miles}{hour}[/tex]
The y-intercept is [tex]b=20\ miles[/tex]
substitute
[tex]y=50x+20[/tex]
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
[tex]120=50x+20[/tex]
[tex]50x=120-20[/tex]
[tex]50x=100[/tex]
[tex]x=2\ hours[/tex]
therefore
The domain is the interval [0,2]
[tex]0\ hours \leq x\leq 2\ hours[/tex]
