Question

Analyze the graph which inequality represents the graph

Answer 1

For this case, we must find two points that belong to the line and thus find the slope.

We have:

We found the slope:

It is also observed that the cut-off point with the y-axis is 4.

In this way, we discard options A and B.

We evaluate option C:

We substitute the point (0,0) that belongs to the shaded region and verify the inequality:

It is not fulfilled!

Thus, the correct option is option D.

ANswer:

Option D

Answer 2

For this case, we must find two points that belong to the line and thus find the slope.

We have:

`(x1, y1) :( 1,1)\\(x2, y2) :(0,4)`

We found the slope:

`m = \frac {y2-y1} {x2-x1} = \frac {4-1} {0-1} = \frac {3} {- 1} = - 3`

It is also observed that the cut-off point with the y-axis is 4.

In this way, we discard options A and B.

We evaluate option C:

`y> -3x + 4`

We substitute the point (0,0) that belongs to the shaded region and verify the inequality:

`0> -3 (0) +4\\0> 4`

It is not fulfilled!

Thus, the correct option is option D.

ANswer:

Option D