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Draw a Cartesian plane with the x and y-axes containing values from -8 to 8. Plot the points below:

Mathematics

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Step-by-step solution

8 steps

1. Plot the points below:
These points are already given in ordered pair format. You should plot them on a Cartesian plane with x and y-axes ranging from -8 to 8.

Part a

(2;−4)(2; -4)

Part b

$(0; 8)$

Part c

(−5;−1)(-5; -1)

Part d

$(8; 7)$

Part e

$(6; 0)$

Part f

(−7;2)(-7; 2)

Part g

(−4;−5)(-4; -5)

Part h· 8 steps

(0;−3)(0; -3)

2. Write an ordered pair to represent each of the points below:
By observing the provided grid:

  • Point A: (−6,3)\boxed{(-6, 3)}
  • Point B: (0,8)\boxed{(0, 8)}
  • Point C: (−4,−3)\boxed{(-4, -3)}
  • Point D: (2,7)\boxed{(2, 7)}
  • Point E: (−8,2)\boxed{(-8, 2)}
  • Point F: (7,−7)\boxed{(7, -7)}
  • Point G: (0,−4)\boxed{(0, -4)}
  • Point H: (4,0)\boxed{(4, 0)}

3. Complete the table of ordered pairs below for the equation: y=x−2y = x - 2
To complete the table, substitute each xx value into the equation y=x−2y = x - 2.

  1. Calculate yy for each xx value.

    • If x=−4x = -4, y=−4−2=−6y = -4 - 2 = -6
    • If x=−3x = -3, y=−3−2=−5y = -3 - 2 = -5
    • If x=−2x = -2, y=−2−2=−4y = -2 - 2 = -4
    • If x=−1x = -1, y=−1−2=−3y = -1 - 2 = -3
    • If x=0x = 0, y=0−2=−2y = 0 - 2 = -2
    • If x=1x = 1, y=1−2=−1y = 1 - 2 = -1
    • If x=2x = 2, y=2−2=0y = 2 - 2 = 0
    • If x=3x = 3, y=3−2=1y = 3 - 2 = 1
    • If x=4x = 4, y=4−2=2y = 4 - 2 = 2

  2. Fill in the table.

    x−4−3−2−101234y-6-5-4-3-2-1012\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \textbf{-6} & \textbf{-5} & \textbf{-4} & \textbf{-3} & \textbf{-2} & \textbf{-1} & \textbf{0} & \textbf{1} & \textbf{2} \\ \hline \end{array}

    Plot the above coordinate points on a Cartesian plane and join the points to form a graph.

    4. Complete the table of ordered pairs below for the equation: y=3x+1y = 3x + 1
    To complete the table, substitute each xx value into the equation y=3x+1y = 3x + 1.

  3. Calculate yy for each xx value.

    • If x=−4x = -4, y=3(−4)+1=−12+1=−11y = 3(-4) + 1 = -12 + 1 = -11
    • If x=−3x = -3, y=3(−3)+1=−9+1=−8y = 3(-3) + 1 = -9 + 1 = -8
    • If x=−2x = -2, y=3(−2)+1=−6+1=−5y = 3(-2) + 1 = -6 + 1 = -5
    • If x=−1x = -1, y=3(−1)+1=−3+1=−2y = 3(-1) + 1 = -3 + 1 = -2
    • If x=0x = 0, y=3(0)+1=0+1=1y = 3(0) + 1 = 0 + 1 = 1
    • If x=1x = 1, y=3(1)+1=3+1=4y = 3(1) + 1 = 3 + 1 = 4
    • If x=2x = 2, y=3(2)+1=6+1=7y = 3(2) + 1 = 6 + 1 = 7
    • If x=3x = 3, y=3(3)+1=9+1=10y = 3(3) + 1 = 9 + 1 = 10
    • If x=4x = 4, y=3(4)+1=12+1=13y = 3(4) + 1 = 12 + 1 = 13

  4. Fill in the table.

    x−4−3−2−101234y-11-8-5-21471013\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \textbf{-11} & \textbf{-8} & \textbf{-5} & \textbf{-2} & \textbf{1} & \textbf{4} & \textbf{7} & \textbf{10} & \textbf{13} \\ \hline \end{array}

    Plot the above coordinate points on a Cartesian plane and join the points to form a graph.

    5. Complete the table of ordered pairs below for the equation: y=x2−4y = x^2 - 4
    To complete the table, substitute each xx value into the equation y=x2−4y = x^2 - 4.

  5. Calculate yy for each xx value.

    • If x=−4x = -4, y=(−4)2−4=16−4=12y = (-4)^2 - 4 = 16 - 4 = 12
    • If x=−3x = -3, y=(−3)2−4=9−4=5y = (-3)^2 - 4 = 9 - 4 = 5
    • If x=−2x = -2, y=(−2)2−4=4−4=0y = (-2)^2 - 4 = 4 - 4 = 0
    • If x=−1x = -1, y=(−1)2−4=1−4=−3y = (-1)^2 - 4 = 1 - 4 = -3
    • If x=0x = 0, y=(0)2−4=0−4=−4y = (0)^2 - 4 = 0 - 4 = -4
    • If x=1x = 1, y=(1)2−4=1−4=−3y = (1)^2 - 4 = 1 - 4 = -3
    • If x=2x = 2, y=(2)2−4=4−4=0y = (2)^2 - 4 = 4 - 4 = 0
    • If x=3x = 3, y=(3)2−4=9−4=5y = (3)^2 - 4 = 9 - 4 = 5
    • If x=4x = 4, y=(4)2−4=16−4=12y = (4)^2 - 4 = 16 - 4 = 12

  6. Fill in the table.

    x−4−3−2−101234y1250-3-4-30512\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \textbf{12} & \textbf{5} & \textbf{0} & \textbf{-3} & \textbf{-4} & \textbf{-3} & \textbf{0} & \textbf{5} & \textbf{12} \\ \hline \end{array}

    Plot the above coordinate points on a Cartesian plane and join the points to form a graph.

    6. Complete the table of ordered pairs below for the equation: y=2x2y = 2x^2
    To complete the table, substitute each xx value into the equation y=2x2y = 2x^2.

  7. Calculate yy for each xx value.

    • If x=−4x = -4, y=2(−4)2=2(16)=32y = 2(-4)^2 = 2(16) = 32
    • If x=−3x = -3, y=2(−3)2=2(9)=18y = 2(-3)^2 = 2(9) = 18
    • If x=−2x = -2, y=2(−2)2=2(4)=8y = 2(-2)^2 = 2(4) = 8
    • If x=−1x = -1, y=2(−1)2=2(1)=2y = 2(-1)^2 = 2(1) = 2
    • If x=0x = 0, y=2(0)2=2(0)=0y = 2(0)^2 = 2(0) = 0
    • If x=1x = 1, y=2(1)2=2(1)=2y = 2(1)^2 = 2(1) = 2
    • If x=2x = 2, y=2(2)2=2(4)=8y = 2(2)^2 = 2(4) = 8
    • If x=3x = 3, y=2(3)2=2(9)=18y = 2(3)^2 = 2(9) = 18
    • If x=4x = 4, y=2(4)2=2(16)=32y = 2(4)^2 = 2(16) = 32

  8. Fill in the table.

    x−4−3−2−101234y3218820281832\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \textbf{32} & \textbf{18} & \textbf{8} & \textbf{2} & \textbf{0} & \textbf{2} & \textbf{8} & \textbf{18} & \textbf{32} \\ \hline \end{array}

    Plot the above coordinate points on a Cartesian plane and join the points to form a graph.

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