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Given the equations and tables below, find the missing values. b. Equation: x = -2y + 6. d. Equation: y = x + 2.

Mathematics

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Graph of y = x + 2

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Key points of y = x + 2
Pointxy
x-intercept−20
y-intercept02

Step-by-step solution

16 steps

Here are the solutions for the remaining parts:

Part b· 4 steps

Equation: x=−2y+6x = -2y + 6

  1. Substitute y=1,2,3y=1, 2, 3 into the equation to find xx.

    For y=1y=1: x=−2(1)+6=−2+6=4x = -2(1) + 6 = -2 + 6 = 4
    For y=2y=2: x=−2(2)+6=−4+6=2x = -2(2) + 6 = -4 + 6 = 2
    For y=3y=3: x=−2(3)+6=−6+6=0x = -2(3) + 6 = -6 + 6 = 0

  2. Substitute y=4y=4 into the equation to find mm.

    m=−2(4)+6=−8+6=−2m = -2(4) + 6 = -8 + 6 = -2

  3. Substitute y=5y=5 into the equation to find xx.

    For y=5y=5: x=−2(5)+6=−10+6=−4x = -2(5) + 6 = -10 + 6 = -4

  4. Substitute x=−174x=-174 into the equation to find nn.

    −174=−2n+6-174 = -2n + 6 −174−6=−2n-174 - 6 = -2n −180=−2n-180 = -2n n=−180−2=90n = \frac{-180}{-2} = 90

    Completed table for b:

    y1234590
    x420-2-4-174

    The value of mm is −2\boxed{-2} and nn is 90\boxed{90}.

Part d· 5 steps

Equation: y=x+2y = x + 2

  1. Substitute x=2x=2 into the equation to find yy.

    y=2+2=4y = 2 + 2 = 4

  2. Substitute y=5y=5 into the equation to find nn.

    5=n+25 = n + 2 n=5−2=3n = 5 - 2 = 3

  3. Substitute x=4,5x=4, 5 into the equation to find yy.

    For x=4x=4: y=4+2=6y = 4 + 2 = 6
    For x=5x=5: y=5+2=7y = 5 + 2 = 7

  4. Substitute x=16x=16 into the equation to find mm.

    m=16+2=18m = 16 + 2 = 18

  5. Substitute x=17x=17 into the equation to find yy.

    y=17+2=19y = 17 + 2 = 19

    Completed table for d:

    x23451617
    y45671819

    The value of nn is 3\boxed{3} and mm is 18\boxed{18}.

Part f· 7 steps

Equation: q=7p−7q = 7p - 7

  1. Substitute p=1,5p=1, 5 into the equation to find qq.

    For p=1p=1: q=7(1)−7=7−7=0q = 7(1) - 7 = 7 - 7 = 0
    For p=5p=5: q=7(5)−7=35−7=28q = 7(5) - 7 = 35 - 7 = 28

  2. Substitute p=10p=10 into the equation to find mm.

    m=7(10)−7=70−7=63m = 7(10) - 7 = 70 - 7 = 63

  3. Substitute p=20p=20 into the equation to find qq.

    q=7(20)−7=140−7=133q = 7(20) - 7 = 140 - 7 = 133

  4. Substitute q=168q=168 into the equation to find nn.

    168=7n−7168 = 7n - 7 168+7=7n168 + 7 = 7n 175=7n175 = 7n n=1757=25n = \frac{175}{7} = 25

  5. Substitute p=100p=100 into the equation to find qq.

    q=7(100)−7=700−7=693q = 7(100) - 7 = 700 - 7 = 693

    Completed table for f:

    p15102025100
    q02863133168693

    The value of mm is 63\boxed{63} and nn is 25\boxed{25}.

    2. What is the value of mm and nn?
    The rule is y=−7x+2y = -7x + 2.

  6. Find the value of mm by substituting y=−145y=-145 into the equation.

    −145=−7m+2-145 = -7m + 2 −145−2=−7m-145 - 2 = -7m −147=−7m-147 = -7m m=−147−7=21m = \frac{-147}{-7} = 21

  7. Find the value of nn by substituting x=60x=60 into the equation.

    n=−7(60)+2n = -7(60) + 2 n=−420+2n = -420 + 2 n=−418n = -418

    The value of mm is 21\boxed{21} and nn is −418\boxed{-418}.

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