Answer:
The system of equation that is represented is:
[tex]y=x^2+6x+7\\\\x+y=1[/tex]
Step-by-step explanation:
It is given that:
a line is graphed through points negative 6 comma 7 and negative 1 comma 2.
i.e. a line passes through (-6,7) and (-1,2).
The equation of line passing through (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(-6,7) and (c,d)= (-1,2).
Hence equation of line is:
[tex]y-7=\dfrac{2-7}{-1+6}\times (x-(-6))\\\\y-7=\dfrac{-5}{5}\times (x+6)\\\\y-7=-1(x+6)\\\\y-7=-x-6\\\\x+y=-6+7\\\\x+y=1[/tex]
Hence, the system of equation that satisfies these two points are:
[tex]y=x^2+6x+7\\\\x+y=1[/tex]
( As in all the other options the equation of line i.e. second equation does not passes through the given points )
