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
let's complete this table and describe the plot. 6.2.1 Copy and Complete the table Step 1: Analyze the given points to find the pattern. We have the points (0, 2), (2, 4), and (4, 6). Let's find the change in y ( y) and the change in x ( x). From (0, 2) to (2, 4): x = 2-0 = 2, y = 4-2 = 2. From (2, 4) to (4, 6): x = 4-2 = 2, y = 6-4 = 2. Since the change in y is constant for a constant change in x, this is a linear relationship. Step 2: Determine the equation of the line. The slope m = ( y)/( x) = (2)/(2) = 1. The y-intercept (c) is the value of y when x=0, which is 2. So, the equation is y = mx + c y = 1x + 2 y = x + 2. Step 3: Use the equation to complete the table. For x=1: y = 1 + 2 = 3. For x=3: y = 3 + 2 = 5. The completed table is: |c|c| x & y \\ 0 & 2 \\ 1 & 3 \\ 2 & 4 \\ 3 & 5 \\ 4 & 6 \\ The final answer for the completed table is: |c|c| x & y \\ 0 & 2 \\ 1 & 3 \\ 2 & 4 \\ 3 & 5 \\ 4 & 6 \\ 6.2.2 Plot points on a Cartesian plan using the table results and join the point. To plot the points, you would mark the following coordinates on a Cartesian plane: (0, 2) (1, 3) (2, 4) (3, 5) (4, 6) After plotting these points, you would draw a straight line connecting them. This line represents the graph of the equation y = x + 2. Drop the next question.