Question

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

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 know it'll have a solid line

Answer 2

how would I graph this?

Answer 3

@happybee @fanton

Answer 4

the origin is 0,0 ....idk how to graph it? please help

Answer 5

@phi can you help?

Answer 6

3x + y greater than or equal to 10.

3x + y >= 10 or
3x + y ≥ 10

I would put it in "slope-intercept" form:
add -3x to both sides:
3x - 3x + y ≥ -3x +10
or, after simplifying

y ≥ -3x +10

Answer 7

we didn't have to do that... but it is easier if you want to plot the line.

in this case, all we have to do is check, does (0,0) "work"?
put y=0 and x=0
y ≥ -3x +10
0 ≥ ? -3*0 + 10
0≥ ? 10

no. 0 is not bigger than 10. so the origin does not work.

Answer 8

you do not want to shade the side that has the origin because the origin does not work

Answer 9

Thank you!! THAT REALLY HELPED ME UNDERSTAND!!! (:

Answer 10

btw, if we just stayed with
3x + y ≥ 10

and plop in (0,0) we get
3*0 + 0 ≥ ? 10
0 ≥ 10 ?
no. the origin does not work.