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
Step 1: Determine the rule for finding Y in the given table 4.1. Based on the table from the previous question, we observe the following (x, Y) pairs: (-2, -5), (-1, -2), (0, 1), (1, 4), (2, 7). For every unit increase in x, the value of Y increases by 3 (e.g., from x=0, Y=1 to x=1, Y=4, Y increases by 4-1=3). This indicates a linear relationship of the form Y = mx + c, where m is the slope. The slope m = 3. To find the y-intercept c, we can use any point from the table, for example, (0, 1): Y = mx + c 1 = 3(0) + c 1 = c Thus, the rule for finding Y is: Y = 3x + 1 Step 2: Test the rule for x = -2. Substitute x = -2 into the rule Y = 3x + 1: Y = 3(-2) + 1 Y = -6 + 1 Y = -5 Step 3: Test the rule for x = -1. Substitute x = -1 into the rule Y = 3x + 1: Y = 3(-1) + 1 Y = -3 + 1 Y = -2 Step 4: Test the rule for x = 0. Substitute x = 0 into the rule Y = 3x + 1: Y = 3(0) + 1 Y = 0 + 1 Y = 1 Step 5: Test the rule for x = 2. Substitute x = 2 into the rule Y = 3x + 1: Y = 3(2) + 1 Y = 6 + 1 Y = 7 Step 6: Test the rule for x = 7. Substitute x = 7 into the rule Y = 3x + 1: Y = 3(7) + 1 Y = 21 + 1 Y = 22 Got more? Send 'em!