Question

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?

2.25
4.00
6.50
17.13

Answer 1

The answer is B

Explanation:

Answer 2

4.00

Explanation:

Given

x: 2 , 5 , 8 , 12

y: 8.50, 15.25, 22.00. 31.00

Required

Determine the y intercept

First, we calculate the slope:

`m = (y_2- y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (2,8,50)`

`(x_2,y_2) = (12,31.00)`

`m = (31.00 - 8.50)/(12 - 2)`

`m = (22.5)/(10)`

`m = 2.25`

Next, we calculate the equation:

`y - y_1 = m(x - x_1)`

Where:

`(x_1,y_1) = (2,8,50)`

`m = 2.25`

The equation becomes:

`y - 8.50 = 2.25(x - 2)`

`y - 8.50 = 2.25x -4.5`

Make y the subject

`y = 2.25x -4.5+8.50`

`y = 2.25x +4`

Take
`x =0`; to get the y intercept

`y = 2.25*0 +4`

`y = 4`

Hence, the y intercept is 4.00