given that the bottom right corner is shaded
first find the equation of the line
find the line passing through (0,-1) and (6,3)
hey, look, when x=0, y=-1, that's the y intercept
y=mx+b, b=y intercept
so y=mx-1 is the equation
now find m
we are given (6,3)
so x=6 and y=3
subsitute
3=6m-1
add 1 both sides
4=6m
divide by 6 both sides
2/3=m
y=2/3x-1 is the equation
ok, so since it is a solid line, it includes the line so our equation is either
[tex]y \geq \frac{2}{3}x-1[/tex] or [tex]y \leq \frac{2}{3}x-1[/tex]
find a point on the bottom left
so maybe 1 below any of the given points
(0,-1) is given point so (0,-2) should work
test any of them
[tex]y \geq \frac{2}{3}x-1[/tex]
[tex]-2 \geq \frac{2}{3}(0)-1[/tex]
[tex]-2 \geq 0-1[/tex]
[tex]-2 \geq -1[/tex]
false
therfor our equation is
[tex]y \leq \frac{2}{3}x-1[/tex]
