Question

Cameron stops to get gas soon after beginning a road trip. He checks his distance

from home 2 hours after filling his gas tank and checks again 3 hours later. The first
time he checked, he was 170 miles from home. The second time, he was 365 miles
from home. What equation models Cameron's distance from home as a function of
the time since getting gas?​

Answer 1

`y=65x+40`

Explanation:

Let

y ----> Cameron's distance from home in miles

x ---> the time in hours since getting gas

we have the ordered pairs

(2,170) and (2+3,365)

so

(2,170) and (5,365)

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(365-170)/(5-2)`

`m=65\ (mi)/(h)` ---> (the slope is the same that the average speed)

Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=65`

`point\ (2,170)`

substitute

`y-170=65(x-2)`

Convert to slope intercept form

`y=mx+b`

Isolate the variable y

`y-170=65x-130\\y=65x-130+170\\y=65x+40`