Answer:
[tex]y=4x[/tex]
Step-by-step explanation:
Let
x ----> the number of miles
y ----> the cost in dollars
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
(2,8) and (3,12)
substitute
[tex]m=\frac{12-8}{3-2}[/tex]
[tex]m=\frac{4}{1}=4[/tex]
Remember that the slope is the same that the unit rate of the linear equation
In this problem the slope means ----> $4 per mile
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=4[/tex]
[tex]point\ (1,4)[/tex]
substitute
[tex]y-4=4(x-1)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y=4x-4+4[/tex]
[tex]y=4x[/tex]
The equation represent a proportional relationship between the variables x and y
