The region is in the first quadrant, and the axis are continuous lines, then x>=0 and y>=0 The region from x=0 to x=1 is below a dashed line that goes through the points: P1=(0,2)=(x1,y1)→x1=0, y1=2 P2=(1,3)=(x2,y2)→x2=1, y2=3 We can find the equation of this line using the point-slope equation: y-y1=m(x-x1) m=(y2-y1)/(x2-x1) m=(3-2)/(1-0) m=1/1 m=1 y-2=1(x-0) y-2=1(x) y-2=x y-2+2=x+2 y=x+2 The region is below this line, and the line is dashed, then the region from x=0 to x=1 is: y<x+2 (Options A or B)
The region from x=2 to x=4 is below the line that goes through the points: P2=(1,3)=(x2,y2)→x2=1, y2=3 P3=(4,0)=(x3,y3)→x3=4, y3=0 We can find the equation of this line using the point-slope equation: y-y3=m(x-x3) m=(y3-y2)/(x3-x2) m=(0-3)/(4-1) m=(-3)/3 m=-1 y-0=-1(x-4) y=-x+4 The region is below this line, and the line is continuos, then the region from x=1 to x=4 is: y<=-x+2 (Option B)
Answer: The system of inequalities would produce the region indicated on the graph is Option B
