Answer:
The line with be duchess with shading below.
None of the above
Step-by-step explanation:
The correct inequality expression is;
y < 2x+3
Note that the inequality sign between the expressions is the one that will determine the nature of the line.
Since the sign is not containing the "equal to" sign this means that the line will be broken(duchess).
Since it is "less than", the shading will be below the line.
Considering the given option, None of the option is correct
For the inequalities
[tex]\rm\bold{ y < 2x+3 ......(1)} \\\\\rm \bold{y > 2x +3....(2)}}[/tex]
For Case (1)
Option d will be chosen as correct option
hence " none of these" will be the answer
For Case (2)
Option b will be chosen as correct option
hence " The line with be duchess with shading above " will be the answer
Since the sign of the inequality here is not clear let us consider 2 cases that are represented by equation (1) and equation (2)
[tex]\rm y < 2x+3 ......(1) \\y > 2x +3....(2)[/tex]
Considering case 1 as represented by equation (1)
The y values are always less than the expression for the line 2x+3 hence points on the line [tex]\rm y = 2x +3[/tex] will not be included for this inequality hence the line will be duchess with area below the line.
So in this case option d will be chosen as correct option
hence " none of these" will be the answer
Similarly now considering case 2 as represented by equation (2)
The y values are always more than the expression for the line 2x+3 hence
points on the line [tex]\rm y = 2x +3[/tex] will not be included for this inequality hence the line will be duchess with area above the line.
So in this case option b will be correct.
Note :
The lines will be solid when the inequalities in equation (1) and (2) also include equal to sign.
That is for lines to be solid
the inequalities will be of type
[tex]\rm y \leq 2x+3 \\y \geq 2x +3[/tex]
For more information please refer to the link below
https://brainly.com/question/11897796
