Question

This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. -28 -54 -21 -40 -14 -26 What is the y-intercept of the line?

Answer 1

y = (0,2)

Explanation:

Answer 2

The y-intercept is y = 2

Explanation:

A linear function has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when
`x = -28, y = -54`

So

`y = mx + b`

`-54 = -28m + b`

`28m = b + 54`

`m = (b + 54)/(28)`

(-21, -40)

This means that when
`x = -21, y = -40`

So

`y = mx + b`

`-40 = -21m + b`

`-40 = -21(b + 54)/(28) + b`

`-40 = (-21b - 1134 + 28b)/(28)`

`7b - 1134 = -40*28`

`7b = 14`

`b = (14)/(7)`

`b = 2`

The y-intercept is y = 2