For the red line, we have:
gradient ([tex]m[/tex]) = 1/3
y-intercept = 3
Equation of straight line is given by [tex]y=mx+c[/tex], where [tex]m[/tex] is the gradient and [tex]c[/tex] is where the line intercept the y-axis
So we have, [tex]y= \frac{1}{3}x+3 [/tex]
The shaded part is above the line, hence the first inequality is
[tex]y \geq \frac{1}{3}x+3 [/tex]
The black line, we have
gradient, [tex](m)[/tex] = 3
y-intercept = -2
[tex]y=mx+c[/tex]
[tex]y=3x-2[/tex], rearranging gives
[tex]3x-y=2[/tex]
The shaded region is to the right of the line, hence the inequality is
[tex]3x-y\ \textgreater \ 2[/tex]
Note: The first option should be the correct answer but the inequality sign for y > 1/3x + 3 should be [tex] \geq [/tex]
