Answer:
6x−y<−3
The graph in the attached figure
Explanation:
Step 1
Find the equation of the line
we have
A(0, 3), B(1, 9)A(0,3),B(1,9)
The formula to calculate the slope between two points is equal to
m=\frac{y2-y1}{x2-x1}m=
x2−x1
y2−y1
substitute
m=\frac{9-3}{1-0}m=
1−0
9−3
m=\frac{6}{1}=6m=
1
6
=6
The equation of the line into slope intercept form is equal to
y=mx+by=mx+b
where
m is the slope
b is the y-intercept
In this problem we have
m=6m=6
b=3b=3 ------> the y-intercept is the point B
substitute
y=6x+3y=6x+3
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
y > 6x+3y>6x+3
rewrite
-6x+y > 3−6x+y>3 ------> multiply by -1−1 both sides
6x-y < -36x−y<−3
Step 3
Using a graphing tool
The x-intercept is the point (-0.5,0)(−0.5,0)
The y-intercept is the point (0,3)(0,3)
The slope of the dashed line is positive
the graph in the attached figure