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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Here are the completed tables of values for each equation. To draw the graphs, you would plot the coordinate pairs (x, y) from each table and connect them with a straight line. Question 3: For each equation, complete the table of values and draw its graph for values of x from -2 to 2. a) y = 3x + 3 Step 1: Substitute each x value into the equation y = 3x + 3. For x = -2, y = 3(-2) + 3 = -6 + 3 = -3. For x = -1, y = 3(-1) + 3 = -3 + 3 = 0. For x = 0, y = 3(0) + 3 = 0 + 3 = 3. For x = 1, y = 3(1) + 3 = 3 + 3 = 6. For x = 2, y = 3(2) + 3 = 6 + 3 = 9. Step 2: Complete the table. |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -3 & 0 & 3 & 6 & 9 \\ The points to plot are (-2, -3), (-1, 0), (0, 3), (1, 6), (2, 9). b) y = x - 9 Step 1: Substitute each x value into the equation y = x - 9. For x = -2, y = -2 - 9 = -11. For x = -1, y = -1 - 9 = -10. For x = 0, y = 0 - 9 = -9. For x = 1, y = 1 - 9 = -8. For x = 2, y = 2 - 9 = -7. Step 2: Complete the table. |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -11 & -10 & -9 & -8 & -7 \\ The points to plot are (-2, -11), (-1, -10), (0, -9), (1, -8), (2, -7). c) y = x - 2 Step 1: Substitute each x value into the equation y = x - 2. For x = -2, y = -2 - 2 = -4. For x = -1, y = -1 - 2 = -3. For x = 0, y = 0 - 2 = -2. For x = 1, y = 1 - 2 = -1. For x = 2, y = 2 - 2 = 0. Step 2: Complete the table. |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -4 & -3 & -2 & -1 & 0 \\ The points to plot are (-2, -4), (-1, -3), (0, -2), (1, -1), (2, 0). d) y = x Step 1: Substitute each x value into the equation y = x. For x = -2, y = -2. For x = -1, y = -1. For x = 0, y = 0. For x = 1, y = 1. For x = 2, y = 2. Step 2: Complete the table. |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -2 & -1 & 0 & 1 & 2 \\ The points to plot are (-2, -2), (-1, -1), (0, 0), (1, 1), (2, 2). Question 4: For each equation, complete the table of values and draw its graph for values of x from -2 to 4. a) y = (1)/(2)x + 1 Step 1: Substitute each x value into the equation y = (1)/(2)x + 1. For x = -2, y = (1)/(2)(-2) + 1 = -1 + 1 = 0. For x = -1, y = (1)/(2)(-1) + 1 = -0.5 + 1 = 0.5. For x = 0, y = (1)/(2)(0) + 1 = 0 + 1 = 1. For x = 1, y = (1)/(2)(1) + 1 = 0.5 + 1 = 1.5. For x = 2, y = (1)/(2)(2) + 1 = 1 + 1 = 2. For x = 3, y = (1)/(2)(3) + 1 = 1.5 + 1 = 2.5. For x = 4, y = (1)/(2)(4) + 1 = 2 + 1 = 3. Step 2: Complete the table. |c|c|c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\ The points to plot are (-2, 0), (-1, 0.5), (0, 1), (1, 1.5), (2, 2), (3, 2.5), (4, 3). b) y = (1)/(4)x + 5 Step 1: Substitute each x value into the equation y = (1)/(4)x + 5. For x = -2, y = (1)/(4)(-2) + 5 = -0.5 + 5 = 4.5. For x = -1, y = (1)/(4)(-1) + 5 = -0.25 + 5 = 4.75. For x = 0, y = (1)/(4)(0) + 5 = 0 + 5 = 5. For x = 1, y = (1)/(4)(1) + 5 = 0.25 + 5 = 5.25. For x = 2, y = (1)/(4)(2) + 5 = 0.5 + 5 = 5.5. For x = 3, y = (1)/(4)(3) + 5 = 0.75 + 5 = 5.75. For x = 4, y = (1)/(4)(4) + 5 = 1 + 5 = 6. Step 2: Complete the table. |c|c|c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ y & 4.5 & 4.75 & 5 & 5.25 & 5.5 & 5.75 & 6 \\ The points to plot are (-2, 4.5), (-1, 4.75), (0, 5), (1, 5.25), (2, 5.5), (3, 5.75), (4, 6). c) y = (1)/(3)x + 1 Step 1: Substitute each x value into the equation y = (1)/(3)x + 1. For x = -2, y = (1)/(3)(-2) + 1 = -(2)/(3) + 1 = (1)/(3). For x = -1, y = (1)/(3)(-1) + 1 = -(1)/(3) + 1 = (2)/(3). For x = 0, y = (1)/(3)(0) + 1 = 0 + 1 = 1. For x = 1, y = (1)/(3)(1) + 1 = (1)/(3) + 1 = (4)/(3). For x = 2, y = (1)/(3)(2) + 1 = (2)/(3) + 1 = (5)/(3). For x = 3, y = (1)/(3)(3) + 1 = 1 + 1 = 2. For x = 4,