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 1: For each equation, complete the table of values and draw its graph for values of x from -1 to 3. a) y = 2x + 1 Step 1: Substitute each x value into the equation y = 2x + 1. For x = -1, y = 2(-1) + 1 = -2 + 1 = -1. For x = 0, y = 2(0) + 1 = 0 + 1 = 1. For x = 1, y = 2(1) + 1 = 2 + 1 = 3. For x = 2, y = 2(2) + 1 = 4 + 1 = 5. For x = 3, y = 2(3) + 1 = 6 + 1 = 7. Step 2: Complete the table. |c|c|c|c|c|c| x & -1 & 0 & 1 & 2 & 3 \\ y & -1 & 1 & 3 & 5 & 7 \\ The points to plot are (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7). b) y = 3x - 1 Step 1: Substitute each x value into the equation y = 3x - 1. For x = -1, y = 3(-1) - 1 = -3 - 1 = -4. For x = 0, y = 3(0) - 1 = 0 - 1 = -1. For x = 1, y = 3(1) - 1 = 3 - 1 = 2. For x = 2, y = 3(2) - 1 = 6 - 1 = 5. For x = 3, y = 3(3) - 1 = 9 - 1 = 8. Step 2: Complete the table. |c|c|c|c|c|c| x & -1 & 0 & 1 & 2 & 3 \\ y & -4 & -1 & 2 & 5 & 8 \\ The points to plot are (-1, -4), (0, -1), (1, 2), (2, 5), (3, 8). c) y = 2x - 3 Step 1: Substitute each x value into the equation y = 2x - 3. For x = -1, y = 2(-1) - 3 = -2 - 3 = -5. For x = 0, y = 2(0) - 3 = 0 - 3 = -3. For x = 1, y = 2(1) - 3 = 2 - 3 = -1. For x = 2, y = 2(2) - 3 = 4 - 3 = 1. For x = 3, y = 2(3) - 3 = 6 - 3 = 3. Step 2: Complete the table. |c|c|c|c|c|c| x & -1 & 0 & 1 & 2 & 3 \\ y & -5 & -3 & -1 & 1 & 3 \\ The points to plot are (-1, -5), (0, -3), (1, -1), (2, 1), (3, 3). d) y = x + 4 Step 1: Substitute each x value into the equation y = x + 4. For x = -1, y = -1 + 4 = 3. For x = 0, y = 0 + 4 = 4. For x = 1, y = 1 + 4 = 5. For x = 2, y = 2 + 4 = 6. For x = 3, y = 3 + 4 = 7. Step 2: Complete the table. |c|c|c|c|c|c| x & -1 & 0 & 1 & 2 & 3 \\ y & 3 & 4 & 5 & 6 & 7 \\ The points to plot are (-1, 3), (0, 4), (1, 5), (2, 6), (3, 7). e) y = 2x Step 1: Substitute each x value into the equation y = 2x. For x = -1, y = 2(-1) = -2. For x = 0, y = 2(0) = 0. For x = 1, y = 2(1) = 2. For x = 2, y = 2(2) = 4. For x = 3, y = 2(3) = 6. Step 2: Complete the table. |c|c|c|c|c|c| x & -1 & 0 & 1 & 2 & 3 \\ y & -2 & 0 & 2 & 4 & 6 \\ The points to plot are (-1, -2), (0, 0), (1, 2), (2, 4), (3, 6). Question 2: For each equation, complete the table of values and draw its graph for values of x from -2 to 3. a) y = 2x + 4 Step 1: Substitute each x value into the equation y = 2x + 4. For x = -2, y = 2(-2) + 4 = -4 + 4 = 0. For x = -1, y = 2(-1) + 4 = -2 + 4 = 2. For x = 0, y = 2(0) + 4 = 0 + 4 = 4. For x = 1, y = 2(1) + 4 = 2 + 4 = 6. For x = 2, y = 2(2) + 4 = 4 + 4 = 8. For x = 3, y = 2(3) + 4 = 6 + 4 = 10. Step 2: Complete the table. |c|c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 & 3 \\ y & 0 & 2 & 4 & 6 & 8 & 10 \\ \