Answer: second option
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Rewrite the expression as:
[tex]3x+y=10[/tex]
Solve for "y":
[tex]y=-3x+10[/tex]
You can identify that:
[tex]m=-3\\b=10[/tex]
Therefore, the line intersects the y-axis at the point (0,10)
For the graphs of inequalities with [tex]\geq\ and\ \leq[/tex] the line must be solid.
The inequality given is [tex]3x+y\geq 10[/tex] and it can be written as [tex]y\geq -3x+10[/tex]
Then, the shaded region must be above the solid line. Therefore it does not include the origin (Observe the graph attached).
