Question

Which system of equations is represented by the graph? a line is graphed through points negative 6 comma 7 and negative 1 comma 2. It intersects a parabola that opens up at these two points. y = x2 − 6x − 7 x − y = 1 y = x2 − 6x + 7 x + y = −1 y = x2 + 6x − 7 x − y = 1 y = x2 + 6x + 7 x + y = 1

Answer 1

The system of equation that is represented is:

`y=x^2+6x+7\\\\x+y=1`

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:

`y-b=(d-b)/(c-a)* (x-a)`

Here (a,b)=(-6,7) and (c,d)= (-1,2).

Hence equation of line is:

`y-7=(2-7)/(-1+6)* (x-(-6))\\\\y-7=(-5)/(5)* (x+6)\\\\y-7=-1(x+6)\\\\y-7=-x-6\\\\x+y=-6+7\\\\x+y=1`

Hence, the system of equation that satisfies these two points are:

`y=x^2+6x+7\\\\x+y=1`

( As in all the other options the equation of line i.e. second equation does not passes through the given points )