Answer:
The graph is a dotted line from ( 0, 12 ) to ( 15 , 0 )
The shaded region is above the boundary line. The origin is not in the shaded region.
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Step-by-step explanation:
x = number of shirts
y = number of pants
16x = amount made from the shirts only
20y = amount made from the pants only
16x+20y = total amount made, aka revenue
16x+20y > 240
This is because Giselle needs to make more than $240 to be profitable.
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The graph is a dotted line because the "or equal to" is not part of the inequality sign. If Giselle could make $240 and be profitable, then we would use a solid line instead and use "or equal to". But in this case, she must make above $240.
Let's consider the boundary line 16x+20y = 240. Plug in x = 0 to get
16x+20y = 240
16*0+20y = 240
20y = 240
y = 240/20
y = 12
Therefore we can say (0,12) is one point on the dotted boundary line. It is the y intercept.
Use similar steps for y = 0 to find x.
16x+20y = 240
16x+20*0 = 240
16x = 240
x = 240/16
x = 15
The x intercept is (15,0) where the dotted line crosses the x axis.
Therefore, the dotted boundary line goes through (0,12) and (15,0).
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Now to the question: where to shade?
Let's check the origin point (0,0). Meaning we plug in x = 0 and y = 0.
16x+20y > 240
16*0+20*0 > 240
0+0 > 240
0 > 240
Clearly that's false so (0,0) is NOT in the shaded solution region. We shade the opposite region of the origin. We'll shade above the boundary as indicated in the diagram below. I used GeoGebra to make the graph. Desmos is another good option.