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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Task 1.1: Complete the tables Equation 1: y = (1)/(2)x + 2 Step 1: Calculate output (y) values for Equation 1. • For x = -2: y = (1)/(2)(-2) + 2 = -1 + 2 = 1 • For x = -1: y = (1)/(2)(-1) + 2 = -0.5 + 2 = 1.5 • For x = 0: y = (1)/(2)(0) + 2 = 0 + 2 = 2 • For x = 0.5: y = (1)/(2)(0.5) + 2 = 0.25 + 2 = 2.25 • For x = 2: y = (1)/(2)(2) + 2 = 1 + 2 = 3 Step 2: Complete the table for Equation 1. |c|c|c|c|c|c| Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ Output (y) & 1 & 1.5 & 2 & 2.25 & 3 \\ Ordered Pair (x; y) & (-2; 1) & (-1; 1.5) & (0; 2) & (0.5; 2.25) & (2; 3) \\ Show your substitution calculations for Equation 1 when: Step 3: Calculate for x = -1. y &= (1)/(2)x + 2 \\ y &= (1)/(2)(-1) + 2 \\ y &= -(1)/(2) + 2 \\ y &= -0.5 + 2 \\ y &= 1.5 Step 4: Calculate for x = 2. y &= (1)/(2)x + 2 \\ y &= (1)/(2)(2) + 2 \\ y &= 1 + 2 \\ y &= 3 Equation 2: y = 2x - 4 Step 5: Calculate output (y) values for Equation 2. • For x = -2: y = 2(-2) - 4 = -4 - 4 = -8 • For x = -1: y = 2(-1) - 4 = -2 - 4 = -6 • For x = 0: y = 2(0) - 4 = 0 - 4 = -4 • For x = 0.5: y = 2(0.5) - 4 = 1 - 4 = -3 • For x = 2: y = 2(2) - 4 = 4 - 4 = 0 Step 6: Complete the table for Equation 2. |c|c|c|c|c|c| Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ Output (y) & -8 & -6 & -4 & -3 & 0 \\ Ordered Pair (x; y) & (-2; -8) & (-1; -6) & (0; -4) & (0.5; -3) & (2; 0) \\ What's next? Send 'em! 📸