Step 1
Find the equation of the line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(0,3)\ B(2,-3)[/tex]
Substitute the values
[tex]m=\frac{-3-3}{2-0}[/tex]
[tex]m=\frac{-6}{2}[/tex]
[tex]m=-3[/tex]
The equation of the line in slope-intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=-3[/tex]
[tex]b=3[/tex] ------> see the graph
substitute
[tex]y=-3x+3[/tex]
Step 2
Find the equation of the inequality
we know that
The solution of the inequality is the shaded area below the solid red line
so
the inequality is
[tex]y\leq -3x+3[/tex]
therefore
the answer is the option C
[tex]y\leq -3x+3[/tex]
