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.
ScanSolve AI Answer
Here is the completed table of values for the relations y_1 = 2x + 5 and y_2 = 3 - 2x: First, calculate the values for y_1 = 2x + 5: For x = -4: y_1 = 2(-4) + 5 = -8 + 5 = -3 For x = -3: y_1 = 2(-3) + 5 = -6 + 5 = -1 For x = -2: y_1 = 2(-2) + 5 = -4 + 5 = 1 For x = -1: y_1 = 2(-1) + 5 = -2 + 5 = 3 For x = 0: y_1 = 2(0) + 5 = 0 + 5 = 5 For x = 1: y_1 = 2(1) + 5 = 2 + 5 = 7 For x = 2: y_1 = 2(2) + 5 = 4 + 5 = 9 For x = 3: y_1 = 2(3) + 5 = 6 + 5 = 11 Next, calculate the values for y_2 = 3 - 2x: For x = -4: y_2 = 3 - 2(-4) = 3 + 8 = 11 For x = -3: y_2 = 3 - 2(-3) = 3 + 6 = 9 For x = -2: y_2 = 3 - 2(-2) = 3 + 4 = 7 For x = -1: y_2 = 3 - 2(-1) = 3 + 2 = 5 For x = 0: y_2 = 3 - 2(0) = 3 - 0 = 3 For x = 1: y_2 = 3 - 2(1) = 3 - 2 = 1 For x = 2: y_2 = 3 - 2(2) = 3 - 4 = -1 For x = 3: y_2 = 3 - 2(3) = 3 - 6 = -3 Here is the completed table: | x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | |-----|----|----|----|----|---|---|---|---| | y_1 | -3 | -1 | 1 | 3 | 5 | 7 | 9 | 11 | | y_2 | 11 | 9 | 7 | 5 | 3 | 1 | -1 | -3 | Table completed as above