Question

Determine the type of boundary line and shading for the graph of the inequality 5x + y greater than or equal to −10. (5 points)

Select one:
a. Dashed line with shading on the side that includes the origin
b. Solid line with shading on the side that does not include the origin
c. Dashed line with shading on the side that does not include the origin
d. Solid line with shading on the side that includes the origin

Answer 1

Answer: The correct answer is d.

Explanation:

Answer 2

The correct answer is d. Solid line with shading on the side that includes the origin

We can tell this for two reasons. Firstly, since it is "greater than or equal to" we use a solid line. If it were just "greater than" than we would have used a dotted line.

Secondly, to tell if the origin should be shaded is by plugging in (0,0) and seeing if it is a true statement. If it is true, it is shaded.

5x + y ≥ -10

5(0) + 0 ≥ -10

0 + 0 ≥ -10

0 ≥ -10 (TRUE)