Answer:
[tex]6x-y< -3[/tex]
The graph in the attached figure
Step-by-step explanation:
Step 1
Find the equation of the line
we have
[tex]A(0, 3), B(1, 9)[/tex]
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{9-3}{1-0}[/tex]
[tex]m=\frac{6}{1}=6[/tex]
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
In this problem we have
[tex]m=6[/tex]
[tex]b=3[/tex] ------> the y-intercept is the point B
substitute
[tex]y=6x+3[/tex]
Step 2
Find the equation of the inequality
we know that
The solution is the shaded area above the dashed line
so
the inequality is equal to
[tex]y>6x+3[/tex]
rewrite
[tex]-6x+y>3[/tex] ------> multiply by [tex]-1[/tex] both sides
[tex]6x-y< -3[/tex]
Step 3
Using a graphing tool
The x-intercept is the point [tex](-0.5,0)[/tex]
The y-intercept is the point [tex](0,3)[/tex]
The slope of the dashed line is positive
the graph in the attached figure
