Question

Which linear inequality is represented by the graph? Oys=x+2 Oy² 2x+2 Oy≤ x+2 Oy²x+2

Answer 1

Answer:

y ≤ $\frac{1}{2}x$ + 2

(first option listed)

Step-by-step explanation:

To quickly find what function is graphed, you can test out one point you find on the graph.

Here, a simple x-value to plug in is 0, because we know it must be equal to 2.

We also know, from what part of the graph is shaded, that this inequality is everything less than that point

(meaning that we should see y ≤ in the inequality)

So, knowing that y must be  ≤   eliminates half of the answer options.

If we plug in 0 to either, we get 2.

So, we need to choose another x-value to evaluate.

We can see that when x = -2, y = 1

We can quickly plug this into both equations

$(\frac{1}{3}) (-2)= \frac{-2}{3}\\\\ \frac{-2}{3} +2 = \frac{4}{3}$

$\frac{4}{3} \neq 1$

-----------------------------------

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

$1 =1$

This means that this graph represents the linear inequality:

y ≤ $\frac{1}{2}$ $x$ + 2