Question

The ordered pair(6,y) is on line AC. Enter the value of y for this ordered pair.

Answer 1

Note: Consider the below figure attached with this question.

Given:

The ordered pair(6,y) is on line AC.

To find:

The y of this ordered pair.

Solution:

From the below figure it is clear that endpoints of AC are A(-7,-4) and C(1,4). So, equation of AC is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-(-4)=(4-(-4))/(1-(-7))(x-(-7))`

`y+4=(4+4)/(1+7)(x+7)`

`y+4=(8)/(8)(x+7)`

`y+4=x+7`

Subtracting 4 from both sides, we get

`y+4-4=x+7-4`

`y=x+3`

Thus, the equation of line AC is
`y=x+3`.

Put x=6 to find the y for the ordered pair (6,y).

`y=6+3`

`y=9`

Therefore, the value of y is 9.