Question

Which equation represents the relationship between the number

of miles traveled and how much it cost?

miles (x) cost (y)
1 $4
2 $8
3 $12
4 $16

Answer 1

`y=4x`

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

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

take the points

(2,8) and (3,12)

substitute

`m=(12-8)/(3-2)`

`m=(4)/(1)=4`

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

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

we have

`m=4`

`point\ (1,4)`

substitute

`y-4=4(x-1)`

step 3

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y=4x-4+4`

`y=4x`

The equation represent a proportional relationship between the variables x and y