Answer:
option A. (1,5)
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area above the dotted line
Remember that
If a ordered pair is a solution of the inequality, then the ordered pair must be satisfy the inequality
Find the equation of the inequality
Find the slope of the dotted line
[tex]m=(-1+3)/(3+3)=1/3[/tex]
The y-intercept is equal to [tex]b=-2[/tex]
The equation of the dotted line is
[tex]y=(1/3)x-2[/tex]
therefore
The equation of the inequality is
[tex]y>(1/3)x-2[/tex]
Verify each case
Substitute the value of x and the value of y in the inequality and then compare the results
case A) (1,5)
[tex]5>(1/3)(1)-2[/tex]
[tex]5>-(5/3)[/tex] ------> is true
therefore
The ordered pair case A is a solution of the inequality
case B) (-3,-3)
[tex]-3>(1/3)(-3)-2[/tex]
[tex]-3>-3[/tex] ------> is not true
therefore
The ordered pair case B is not a solution of the inequality
case C) (3,-1)
[tex]-1>(1/3)(3)-2[/tex]
[tex]-1>-1[/tex] ------> is not true
therefore
The ordered pair case C is not a solution of the inequality
case D) (5,-5)
[tex]-5>(1/3)(5)-2[/tex]
[tex]-5>-1/3[/tex] ------> is not true
therefore
The ordered pair case D is not a solution of the inequality
