Question

What system of linear inequalities is shown in the graph? Enter your answers in the boxes.

Answer 1

Step 1

Find the slope of the dotted line A

Let

$A(-3,1)\\B(0,2)$

Find the slope m

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute in the formula

$m=\frac{(2-1)}{(0+3)}$

$m=\frac{(1)}{(3)}$

$mA=\frac{1}{3}$

Step 2

Find the equation of the line A

we know that

$y-y1=m(x-x1)$

we have

$mA=\frac{1}{3}$

$B(0,2)$

substitute

$y-2=\frac{1}{3}(x-0)$

$y=\frac{1}{3}x+2$

Step 3

Find the equation of the inequality A

we know that

the solution is below the dotted line A

so

the inequality A is    

$y$

Step 4

Find the slope of the solid line B

Let

$B(0,2)\\C(1,0)$

Find the slope m

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute in the formula

$m=\frac{(0-2)}{(1-0)}$

$m=\frac{(-2)}{(1)}$

$mB=-2$

Step 5

Find the equation of the line B

we know that

$y-y1=m(x-x1)$

we have

$mB=-2$

$B(0,2)$

substitute

$y-2=-2(x-0)$

$y=-2x+2$

Step 6

Find the equation of the inequality B

we know that

the solution is below the solid line B

so

the inequality B is    

$y\leq -2x+2$

therefore

The system of linear inequalities is

$y$

$y\leq -2x+2$

using a graphing tool

the solution is the shaded area

see the attached figure

Answer 2

First, find the equation of the lines:

y=-2x+2 and y=1/3x+2

We see that the shaded part is below the y=1/3x+2 graph, so it becomes y<1/3x+2 (It's not ≤ since it's a dotted line)

For the y=-2x+2, the shaded part is under the line as well, so it becomes y≤-2x+2 (Here, we include the ≤ since it's a solid line)

So your answer is y<1/3x+2 and y≤-2x+2.