Question

Which is the graph of the linear inequality y ≥ −x − 3?

Answer 1

Answer:

Option A is correct.

Step-by-step explanation:

An inequality on a coordinate plane consist of a boundary line and an area in which each point is a possible solution.

* If the inequality has a sign $'\geq'$ or $'\leq'$ , then the line will be a solid line and its point are included in the solution.

* If the inequality has a sign '>' or '<' , then the line will be a dotted line and its point are not  included in the solution.

Given: The linear inequality: $y\geq -x-3$

Then, the equation of the boundary line is; y = -x - 3                .....[1]

Compare this  boundary line equation with the general point slope intercept line i.e, y = mx+b where m is the slope and b is the y-intercept.

Therefore, the slope of the this line is, m = -1

and a y-intercept (b) = -3  

To find x -intercept:

Substitute y =0 in [1] to solve for x;

0= -x -3

Add 3 both sides, we get

0+3 = -x -3+3

Simplify:

3 = -x

or

x = -3

Therefore, the x-intercept is -3

Now,

Plot y = -x -3  ( as a solid line because $y\geq$ included equal to)

and shade the area above as $y\geq -x-3$ as shown below in the graph.

Answer 2

It's te 1st graph. Why?

The inequality is y ≥ −x − 3, it means could be EQUAL OR Greater than -x-3
Then the line is consistent, where the 3rd graph shows that the line is dotted, that mean it's ONLY greater & can't be equal