Question

Which correctly describes how the graph of the inequality 5x + 2y ≥ 13 is shaded? (1 point) Above the solid line Below the solid line Above the dashed line Below the dashed line

Answer 1

The answer is above the solid line.
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Answer 2

The graph of inequality
`5x+2y\geq 13` is above the solid line.

Explanation:

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 or , 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:
`5x+2y\geq 13`

Then, the equation of the boundary line is; 5x+2y =13 ......[1]

we can write this as;

`2y = -5x+13`

Divide by 2 we get;

`y = -(5)/(2) x + (13)/(2)` ......[2]

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 =
`-(5)/(2)`

and a y-intercept (b) =
`(13)/(2)` = 6.5

To find x -intercept:

Substitute y =0 in to solve for x;

`5x+0 =13`

Simplify:

`x =(13)/(5) = 2.6`

Therefore, the x-intercept is 2.6

Now,

Plot
`y = -(5)/(2) x + (13)/(2)` ( as a solid line because
`y\geq` included equal to)

and shade the area above as
`5x+2y\geq 13` as shown below in the graph