Answer:
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
