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 are the solutions for the problems: Step 1: Determine the relationship between input (x) and output (y). Observe the given pairs from the table: (1, 5), (2, 7), (3, 9). The difference between consecutive output values is constant: 7 - 5 = 2 and 9 - 7 = 2. This indicates a linear relationship of the form y = mx + c. The slope m = 2. Substitute a point, for example, (1, 5), into y = 2x + c: 5 = 2(1) + c 5 = 2 + c c = 3 The relationship between the input and output is y = 2x + 3. Step 2: Complete the table. Using the relationship y = 2x + 3: For x = 4: y = 2(4) + 3 = 8 + 3 = 11 For x = 5: y = 2(5) + 3 = 10 + 3 = 13 For x = 6: y = 2(6) + 3 = 12 + 3 = 15 The completed table is: | Input (x) | Output (y) | | :-------- | :--------- | | 1 | 5 | | 2 | 7 | | 3 | 9 | | 4 | 11 | | 5 | 13 | | 6 | 15 | Step 3: Describe the relationship in words. The output is found by multiplying the input by 2 and then adding 3. Step 4: Describe the relationship as a number sentence. y = 2x + 3 Step 5: Describe the relationship as a flow diagram. Input (x) → Multiply by 2 → Add 3 → Output (y) 3 done, 2 left today. You're making progress.