Which system of inequalities is represented by the graph? i need help on this for a test

Line 1:

We know that the dotted line is the first equation since it is the only one without an 'equal to'

We can see that the y-intercept of the line is '+2'

Now to find its slope

since slope is rise/run and we see that the slope goes down 4 units while travelling only 2 units on the x plane

So, the slope  = -2

Hence, it's formula is y _ -2x  +2

i left a dash in the equation to explain why it will be a '<'

In the graph, we can see that the shaded region is the area where values of all the graphs overlap

Hence, for the area of overlap to be below our line 1, the symbol is <

Therefore, the equation for line 1:

y < -2x + 2

This eliminated option 1 and 4 since their equation is different

Line 2:

Again in this one, the symbol will be a less than since the area of overlap is below the line but since the line is not dotted,

the symbol will be ≤ (less than or equal to)

One of the 2 remaining lines is linear and since the line in question is not linear, we know which line we are talking about

Now to find its equation

y-intercept = -1

Slope = Rise / Run

Since its y increases by 1 whenever the x increases by 2

Rise = 1      Run = 2

Slope = 1/2

Equation:

y ≤ x/2 -1

Now that we have 2 of the 3 equations, we are basically done

We can see that the only system of inequalities that satisfies our equations is 2

Hence, option 'b' is correct

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

it would take 7/10 of an hour too fill the pool.

step-by-step explanation: