Question

Determine the type of boundary line and shading for the graph of the inequality 3x + y greater than or equal to 10.

Answer 1

Answer: second option

Step-by-step explanation:

The equation of the line in slope-intercept form is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

Rewrite the expression as:

$3x+y=10$

Solve for "y":

$y=-3x+10$

You can identify that:

$m=-3\\b=10$

Therefore, the line intersects the y-axis at the point (0,10)

For the graphs of inequalities with $\geq\ and\ \leq$ the line must be solid.

The inequality given is $3x+y\geq 10$ and it can be written as $y\geq -3x+10$

Then, the shaded region must be above the solid line. Therefore  it does not include the origin (Observe the graph attached).