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First, calculate the values for y₁ = 2x + 5:

Mathematics

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Table completed as above\text{Table completed as above}

Here is the completed table of values for the relations y1=2x+5y_1 = 2x + 5 and y2=3−2xy_2 = 3 - 2x:

First, calculate the values for y1=2x+5y_1 = 2x + 5:

  • For x=−4x = -4: y1=2(−4)+5=−8+5=−3y_1 = 2(-4) + 5 = -8 + 5 = -3
  • For x=−3x = -3: y1=2(−3)+5=−6+5=−1y_1 = 2(-3) + 5 = -6 + 5 = -1
  • For x=−2x = -2: y1=2(−2)+5=−4+5=1y_1 = 2(-2) + 5 = -4 + 5 = 1
  • For x=−1x = -1: y1=2(−1)+5=−2+5=3y_1 = 2(-1) + 5 = -2 + 5 = 3
  • For x=0x = 0: y1=2(0)+5=0+5=5y_1 = 2(0) + 5 = 0 + 5 = 5
  • For x=1x = 1: y1=2(1)+5=2+5=7y_1 = 2(1) + 5 = 2 + 5 = 7
  • For x=2x = 2: y1=2(2)+5=4+5=9y_1 = 2(2) + 5 = 4 + 5 = 9
  • For x=3x = 3: y1=2(3)+5=6+5=11y_1 = 2(3) + 5 = 6 + 5 = 11

Next, calculate the values for y2=3−2xy_2 = 3 - 2x:

  • For x=−4x = -4: y2=3−2(−4)=3+8=11y_2 = 3 - 2(-4) = 3 + 8 = 11
  • For x=−3x = -3: y2=3−2(−3)=3+6=9y_2 = 3 - 2(-3) = 3 + 6 = 9
  • For x=−2x = -2: y2=3−2(−2)=3+4=7y_2 = 3 - 2(-2) = 3 + 4 = 7
  • For x=−1x = -1: y2=3−2(−1)=3+2=5y_2 = 3 - 2(-1) = 3 + 2 = 5
  • For x=0x = 0: y2=3−2(0)=3−0=3y_2 = 3 - 2(0) = 3 - 0 = 3
  • For x=1x = 1: y2=3−2(1)=3−2=1y_2 = 3 - 2(1) = 3 - 2 = 1
  • For x=2x = 2: y2=3−2(2)=3−4=−1y_2 = 3 - 2(2) = 3 - 4 = -1
  • For x=3x = 3: y2=3−2(3)=3−6=−3y_2 = 3 - 2(3) = 3 - 6 = -3

Here is the completed table:

xx-4-3-2-10123
y1y_1-3-11357911
y2y_21197531-1-3
Table completed as above\text{Table completed as above}
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