case A)
If the inequality is
[tex]y< x-2[/tex] ------> inequality
we know that
The solution of the inequality is the shaded area below the dotted line
The equation of the line is [tex]y= x-2[/tex]
The slope is positive and equal to [tex]m=1[/tex]
The x-intercept is the point [tex](2,0)[/tex] -----> the value of x when the value of y is equal to zero
The y-intercept is the point [tex](0,-2)[/tex] -----> the value of y when the value of x is equal to zero
therefore
the answer in the attached figure N 1
case B)
If the inequality is
[tex]y< \frac{1}{3} x-2[/tex] ------> inequality
we know that
The solution of the inequality is the shaded area below the dotted line
The equation of the line is [tex]y=\frac{1}{3}x-2[/tex]
The slope is positive and equal to [tex]m=\frac{1}{3}[/tex]
The x-intercept is the point [tex](6,0)[/tex] -----> the value of x when the value of y is equal to zero
The y-intercept is the point [tex](0,-2)[/tex] -----> the value of y when the value of x is equal to zero
therefore
the answer in the attached figure N 2
