Question

Find the inequality represented by the graph

Answer 1

the answer is y ≥ 1/2x

Answer 2

`y\geq (1)/(2)x`

Explanation:

To find the inequality represent by the graph, we first must find the linear equation that represents that line.

So, in first place, we find the slope of the line, using two point (0,0) and (2,1):

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )=(1-0)/(2-0)=(1)/(2)`

Now, using one point, the slope and the slope-point formula, we find the linear expression

`y-y_(1)=m(x-x_(1))\\y-0=(1)/(2)(x-0)\\ y=(1)/(2)x`

Then, with the linear expression, we just need to take a test point form the shaded area and evaluate the expression, the point is gonna be (0,1):

`y=(1)/(2)x\\1=(1)/(2)(0)\\ 1=0`

We know that 1 is more than zero, this means that the right inequality sign is
`\geq`, due to the relation of the numbers, and because line is solid.

Therefore, the inequality is

`y\geq (1)/(2)x`