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Copy and complete the table of values for the relations y1 = 2x + 5 and y2 = 3 − 2x for x from -4 to 3.

Mathematics

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  1. Complete the table of values for y1=2x+5y_1 = 2x + 5.

    We substitute each xx value into the function y1=2x+5y_1 = 2x + 5.

    For x=−3x = -3:

    y1=2(−3)+5=−6+5=-1y_1 = 2(-3) + 5 = -6 + 5 = \boxed{\textbf{-1}}

    For x=−2x = -2:

    y1=2(−2)+5=−4+5=1y_1 = 2(-2) + 5 = -4 + 5 = \boxed{\textbf{1}}

    For x=0x = 0:

    y1=2(0)+5=0+5=5y_1 = 2(0) + 5 = 0 + 5 = \boxed{\textbf{5}}

    For x=2x = 2:

    y1=2(2)+5=4+5=9y_1 = 2(2) + 5 = 4 + 5 = \boxed{\textbf{9}}

    For x=3x = 3:

    y1=2(3)+5=6+5=11y_1 = 2(3) + 5 = 6 + 5 = \boxed{\textbf{11}}
  2. Complete the table of values for y2=3−2xy_2 = 3 - 2x.

    We substitute each xx value into the function y2=3−2xy_2 = 3 - 2x.

    For x=−2x = -2:

    y2=3−2(−2)=3+4=7y_2 = 3 - 2(-2) = 3 + 4 = \boxed{\textbf{7}}

    For x=0x = 0:

    y2=3−2(0)=3−0=3y_2 = 3 - 2(0) = 3 - 0 = \boxed{\textbf{3}}

    For x=1x = 1:

    y2=3−2(1)=3−2=1y_2 = 3 - 2(1) = 3 - 2 = \boxed{\textbf{1}}

    For x=2x = 2:

    y2=3−2(2)=3−4=-1y_2 = 3 - 2(2) = 3 - 4 = \boxed{\textbf{-1}}

    For x=3x = 3:

    y2=3−2(3)=3−6=-3y_2 = 3 - 2(3) = 3 - 6 = \boxed{\textbf{-3}}

    Note: The value for y2y_2 at x=3x=3 in the original table is given as 11, which contradicts the relation y2=3−2xy_2 = 3 - 2x. The calculated value is -3.

    The completed table is:

    X-4-3-2-10123
    y1=2x+5y_1 = 2x + 5-3-11357911
    y2=3−2xy_2 = 3 - 2x1197531-1-3
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