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
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-4)=\dfrac{4-(-4)}{1-(-7)}(x-(-7))[/tex]
[tex]y+4=\dfrac{4+4}{1+7}(x+7)[/tex]
[tex]y+4=\dfrac{8}{8}(x+7)[/tex]
[tex]y+4=x+7[/tex]
Subtracting 4 from both sides, we get
[tex]y+4-4=x+7-4[/tex]
[tex]y=x+3[/tex]
Thus, the equation of line AC is [tex]y=x+3[/tex].
Put x=6 to find the y for the ordered pair (6,y).
[tex]y=6+3[/tex]
[tex]y=9[/tex]
Therefore, the value of y is 9.
