Answer:
1) Point [tex](1,0)[/tex] -----> see the attached figure N [tex]1[/tex]
2) The value of x is [tex]4[/tex]
3) I quadrant
4) [tex](1,1)[/tex]
5) [tex]y>-5x+3[/tex]
Step-by-step explanation:
Part 1)
we know that
If the point satisfy the inequality
then
the point must be included in the shaded area
The point [tex](1,0)[/tex] is included in the shaded area
Part 2)
we have
[tex]x-2y\geq 4[/tex]
see the attached figure N [tex]2[/tex]
we know that
The value for x on the boundary line and the x axis is equal to the x-intercept of the line [tex]x-2y= 4[/tex]
For [tex]y=0[/tex]
Find the value of x
[tex]x-2(0)= 4[/tex]
[tex]x=4[/tex]
The solution is [tex]x=4[/tex]
Part 3)
we have
[tex]x\geq 0[/tex] -----> inequality A
The solution of the inequality A is in the first and fourth quadrant
[tex]y\geq 0[/tex] -----> inequality B
The solution of the inequality B is in the first and second quadrant
so
the solution of the inequality A and the inequality B is the first quadrant
Part 4) Which ordered pair is a solution of the inequality?
we have
[tex]y\geq 4x-5[/tex]
we know that
If a ordered pair is a solution of the inequality
then
the ordered pair must be satisfy the inequality
we're going to verify all the cases
case A) point [tex](3,4)[/tex]
Substitute the value of x and y in the inequality
[tex]x=3,y=4[/tex]
[tex]4\geq 4(3)-5[/tex]
[tex]4\geq 7[/tex] ------> is not true
therefore
the point [tex](3,4)[/tex] is not a solution of the inequality
case B) point [tex](2,1)[/tex]
Substitute the value of x and y in the inequality
[tex]x=2,y=1[/tex]
[tex]1\geq 4(2)-5[/tex]
[tex]1\geq 3[/tex] ------> is not true
therefore
the point [tex](2,1)[/tex] is not a solution of the inequality
case C) point [tex](3,0)[/tex]
Substitute the value of x and y in the inequality
[tex]x=3,y=0[/tex]
[tex]0\geq 4(3)-5[/tex]
[tex]0\geq 7[/tex] ------> is not true
therefore
the point [tex](3,0)[/tex] is not a solution of the inequality
case D) point [tex](1,1)[/tex]
Substitute the value of x and y in the inequality
[tex]x=1,y=1[/tex]
[tex]1\geq 4(1)-5[/tex]
[tex]1\geq -1[/tex] ------> is true
therefore
the point [tex](1,1)[/tex] is a solution of the inequality
Part 5) Write an inequality to match the graph
we know that
The equation of the line has a negative slope
The y-intercept is the point [tex](3,0)[/tex]
The x-intercept is a positive number
The solution is the shaded area above the dashed line
so
the equation of the line is [tex]y=-5x+3[/tex]
The inequality is [tex]y>-5x+3[/tex]
