In the table below, x represents miles traveled and y represents the cost to travel by train. miles, x cost, y 2 8.50 5 15.25 8 22.00 12 31.00 what is the y-intercept of this function?

4

Step-by-step explanation:

a linear function is

y = ax + b

so, for the first pair of x, y

8.5 = 2a + b

b = 8.5 - 2a

the second pair

15.25 = 5a + b

let's use the substitution information from the first pair :

15.25 = 5a + 8.5 - 2a

6.75 = 3a

a = 2.25

b = 8.5 - 2×2.25 = 8.5 - 4.5 = 4

so, we get as linear function

y = 2.25x + 4

that means the y-intercept (x = 0) is at y = 4

y = 2.25×0 + 4 = 4

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