Question

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

answer choices
Dashed line with shading on the side that includes the origin
Solid line with shading on the side that does not include the origin
Dashed line with shading on the side that does not include the origin
Solid line with shading on the side that includes the origin

Answer 1

i agree with the second option

Explanation:

Answer 2

Answer: second option

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).