we have the inequality
3x - y < - 6
isolate the variable y
subtract 3x both sides
-y< -3x-6
multiply by -1 both sides
y > 3x+6
the solution is the shaded area above the dashed line y=3x+6
so
to graph the inequality
graph the dashed line y=3x+6 and shaded the area above
To graph the dashed line we need two points
Find out the intercepts
y-intercept (value of y when the value of x=0)
For x=0
y=3(0)+6
y=6
the y-intercept is the point (0,6)
Find out the x-intercept
For y=0
0=3x+6
3x=-6
x=-2
the x-intercept is the point (-2,0)
Graph the dashed line
using a graphing tool
see the attached figure
the solution is all real number that lies on the shaded area
Test point
point (-2,6)
the point (-2,6) lies on the shaded area
Verify
substitute x=-2 and y=6 in the inequality
3x - y < - 6
3(-2)-6 < -6
-12 < -6 -----> is true
that means ----> is a solution
Prove with point (5,5)
the point (5,5) does not lie on the shaded area
3(5)-5 < -6
10< -6 -----> is not true
that means -----> is not a solution