Q1. 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.

a. y = x^2 − 6x − 7
x − y = 1

b. y = x^2 − 6x + 7
x + y = −1

c. y = x^2 + 6x − 7
x − y = 1

d. y = x^2 + 6x + 7
x + y = 1

Let

we know that

The points A and B must satisfy both equations

we proceed to verify each case

case A)

equation

check point A

for

y must be

substitute

is not equal to

so

The system of equations is not represented by the graph

It is not necessary to check point B

case B)

equation

check point A

for

y must be

substitute

is not equal to

so

The system of equations is not represented by the graph

It is not necessary to check point B

case C)

equation

check point A

for

y must be

substitute

is not equal to

so

The system of equations is not represented by the graph

It is not necessary to check point B

case D)

equation

check point A

for

y must be

substitute

is equal to ------->is ok

check point B

for

y must be

substitute

is equal to ----->is ok

equation

check point A

for

y must be

substitute

is equal to ------->is ok

check point B

for

y must be

substitute

is equal to ----->is ok

therefore

the answer is the option D

b.an increase in a causes b to decrease