Answer:
[tex]y=65x+40[/tex]
Step-by-step 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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{365-170}{5-2}[/tex]
[tex]m=65\ \frac{mi}{h}[/tex] ---> (the slope is the same that the average speed)
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=65[/tex]
[tex]point\ (2,170)[/tex]
substitute
[tex]y-170=65(x-2)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-170=65x-130\\y=65x-130+170\\y=65x+40[/tex]
