Question

Which linear inequality is represented by the graph

Answer 1

`y\leq (1)/(2) x+2`

Explanation:

Firstly, as seen in the graph, the shaded area is below the graph. This means that
`y \leq`

Next we can look at the slope. It is seen that m=
`(1)/(2)`

From these two observations, the only inequality that fits the critera is

`y\leq (1)/(2) x+2`

Answer 2

Option A

Explanation:

(1) In the given graph a solid line has been given which represent the sign of inequality between two variables.

(2) Moreover this, a should area has been given below the solid line. which represents the sign of "less than" between the variables.

In total between y and x there should be a sign of (≤)

(3) Now this line passes through two points (0,2) and (-4,0) so slope of the line will be =
`(y-y')/(x-x')`

Therefore, slope =
`(2-0)/(0+4)=(1)/(2)`

y-intercept of the line has been given as 2

So inequality for this graph will be

y ≤
`(1)/(2)`x + 2

Option A is the answer.