Question

The graph below shows the solution to a system of inequalities. Which of the inequalities is modeled by the graph?y < -x + 4 y >/ 2x + 4 y < -x + 4 y 2x + 4 y > -x + 4y >/ 2x + 4 y -x + 4 y > 2x + 4

Answer 1

We need to find the system of inequalities modeled by the graph.

At first, we will find the equations of the lines:

The general equation of the line is : y = mx + b

where m is the slope and b is y - intercept

The equation of the red solid line:

the line passing through the points (-2 , 0) and (0,4)

The slope = rise/run = 4/2 = 2

b = y- intercept = 4

so, the equation of the line is : y = 2x + 4

As the shaded area on the left of the line, the inequality will be:

`y\ge2x+4`

Now, finding the equation of the dash blue line:

The line passing through the points ( 4 , 0 ) , ( 0 , 4 )

The slope = rise/run = 4/-4 = -1

b = y- intercept = 4

so, the equation of the line is : y = -x + 4

So, the inequality will be:

`y<-x+4`

So, the system of inequalities modeled by the graph is:

`\begin{gathered} y\ge2x+4 \\ y<-x+4 \end{gathered}`

So, the answer is option A.