This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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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. a) (2; -4) b) (0; 8) c) (-5; -1) d) (8; 7) e) (6; 0) f) (-7; 2) g) (-4; -5) h) (0; -3) 2. Write an ordered pair to represent each of the points below: By observing the provided grid: Point A: (-6, 3) Point B: (0, 8) Point C: (-4, -3) Point D: (2, 7) Point E: (-8, 2) Point F: (7, -7) Point G: (0, -4) Point H: (4, 0) 3. Complete the table of ordered pairs below for the equation: y = x - 2 To complete the table, substitute each x value into the equation y = x - 2. Step 1: Calculate y for each x value. If x = -4, y = -4 - 2 = -6 If x = -3, y = -3 - 2 = -5 If x = -2, y = -2 - 2 = -4 If x = -1, y = -1 - 2 = -3 If x = 0, y = 0 - 2 = -2 If x = 1, y = 1 - 2 = -1 If x = 2, y = 2 - 2 = 0 If x = 3, y = 3 - 2 = 1 If x = 4, y = 4 - 2 = 2 Step 2: Fill in the table. |c|c|c|c|c|c|c|c|c|c| x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & -6 & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 \\ 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 + 1 To complete the table, substitute each x value into the equation y = 3x + 1. Step 1: Calculate y for each x value. If x = -4, y = 3(-4) + 1 = -12 + 1 = -11 If x = -3, y = 3(-3) + 1 = -9 + 1 = -8 If x = -2, y = 3(-2) + 1 = -6 + 1 = -5 If x = -1, y = 3(-1) + 1 = -3 + 1 = -2 If x = 0, y = 3(0) + 1 = 0 + 1 = 1 If x = 1, y = 3(1) + 1 = 3 + 1 = 4 If x = 2, y = 3(2) + 1 = 6 + 1 = 7 If x = 3, y = 3(3) + 1 = 9 + 1 = 10 If x = 4, y = 3(4) + 1 = 12 + 1 = 13 Step 2: Fill in the table. |c|c|c|c|c|c|c|c|c|c| x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & -11 & -8 & -5 & -2 & 1 & 4 & 7 & 10 & 13 \\ 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 = x^2 - 4 To complete the table, substitute each x value into the equation y = x^2 - 4. Step 1: Calculate y for each x value. If x = -4, y = (-4)^2 - 4 = 16 - 4 = 12 If x = -3, y = (-3)^2 - 4 = 9 - 4 = 5 If x = -2, y = (-2)^2 - 4 = 4 - 4 = 0 If x = -1, y = (-1)^2 - 4 = 1 - 4 = -3 If x = 0, y = (0)^2 - 4 = 0 - 4 = -4 If x = 1, y = (1)^2 - 4 = 1 - 4 = -3 If x = 2, y = (2)^2 - 4 = 4 - 4 = 0 If x = 3, y = (3)^2 - 4 = 9 - 4 = 5 If x = 4, y = (4)^2 - 4 = 16 - 4 = 12 Step 2: Fill in the table. |c|c|c|c|c|c|c|c|c|c| x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & 12 & 5 & 0 & -3 & -4 & -3 & 0 & 5 & 12 \\ 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 = 2x^2 To complete the table, substitute each x value into the equation y = 2x^2. Step 1: Calculate y for each x value. If x = -4, y = 2(-4)^2 = 2(16) = 32 If x = -3, y = 2(-3)^2 = 2(9) = 18 If x = -2, y = 2(-2)^2 = 2(4) = 8 If x = -1, y = 2(-1)^2 = 2(1) = 2 If x = 0, y = 2(0)^2 = 2(0) = 0 If x = 1, y = 2(1)^2 = 2(1) = 2 If x = 2, y = 2(2)^2 = 2(4) = 8 If x = 3, y = 2(3)^2 = 2(9) = 18 If x = 4, y = 2(4)^2 = 2(16) = 32 Step 2: Fill in the table. |c|c|c|c|c|c|c|c|c|c| x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & 32 & 18 & 8 & 2 & 0 & 2 & 8 & 18 & 32 \\ Plot the above coordinate points on a Cartesian plane and join the points to form a graph. What's next? 📸