The equation of a straight line is given by [tex]y=mx+c[/tex], where [tex]m[/tex] is the gradient of the slope and [tex]c[/tex] is the y-intercept
We pick two coordinates (5, 0.5) and (0, -1.5)
Gradient = [tex] \frac{difference-in-y}{difference-in-x} [/tex]
Gradient = [tex] \frac{-1.5-0.5}{0-5} = \frac{-2}{-5} = \frac{2}{5} [/tex]
The graph crosses y-axis at -1.5
[tex]y=mx+c[/tex]
[tex]y= \frac{2}{5} x-1.5[/tex], multiply each term by 2 gives
[tex]2y= \frac{4}{5}x-3 [/tex], rearranging
[tex] \frac{4}{5}x-2y=3 [/tex]
The shaded area is below the line, hence the inequality is
[tex] \frac{4}{5}x-2y \leq 3[/tex]
