Question

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Which linear inequality is represented by the graph?


y ≤ x + 2

y ≥ x + 2

y ≤ x + 2

y ≥ x + 2

Answer 1

I have graphed these for you, I am sure you can tell which is which now!

Hope this helps!

Answer 2

Step 1

Find the slope of the line

Let    

$A(-4,0)\\B(0,2)$

we know that

the formula to calculate the slope between two points is equal to

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

substitute the values

$m=\frac{(2-0)}{(0+4)}$

$m=\frac{(2)}{(4)}$

$m=\frac{1}{2}$

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

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

we have

$(x1,y1)=(0.2)$

$m=\frac{1}{2}$

substitute the values

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

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

Step 3

Find the linear inequality represented by the graph

we know that

in the graph the solution is the shaded area below the solid line

that means

the inequality  is equal to

$y \leq \frac{1}{2}x+2$

therefore

the answer is

$y \leq \frac{1}{2}x+2$