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Which graph represents the system of inequalities?

AngelRay  Mar 3, 2018
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AngelRay, my strategy here would be to convert all inequalities to slope-intercept form (\(y=mx+b\)). Converting to slope-intercept form is useful because the form gives one information about how a graph should look. I can, then, compare this information with the four graphs given.

 

\(x-y<-1\) Add x to both sides.
\(-y<-x-1\) Divide by -1 on both sides. Doing this causes an equality signage change.
\(y>x+1\)  
   

 

The point-intercept form gives us some information about the corresponding graph of this equation. I will name two of these.

 

  • The slope is 1
  • The y-intercept is located at \((1,0)\)

Every graph appears to have the correct slope, but the coordinate of the y-intercept changes from graph to graph. Only the first and last graphs have a y-intercept of \((1,0)\) . Therefore, we have already eliminated two graphs from the list. Notice that the inequality would result in a dashed line. Only the last graph accounts for this technicality, so the bottom-right one is the correct graph.

TheXSquaredFactor  Mar 4, 2018

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