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 steps to plot the graphs and find the line of symmetry, formatted for you to easily transfer to your graph sheet. Step 1: Create a table of values for the function y = 2x + 1. Choose integer values for x to get clear points. |c|c|c| x & y = 2x + 1 & (x, y) \\ -2 & 2(-2) + 1 = -3 & (-2, -3) \\ -1 & 2(-1) + 1 = -1 & (-1, -1) \\ 0 & 2(0) + 1 = 1 & (0, 1) \\ 1 & 2(1) + 1 = 3 & (1, 3) \\ 2 & 2(2) + 1 = 5 & (2, 5) \\ Step 2: Create a table of values for the function y = (x-1)/(2). Choose values for x that make (x-1) an even number to get integer or half-integer y values. |c|c|c| x & y = (x-1)/(2) & (x, y) \\ -3 & (-3-1)/(2) = -2 & (-3, -2) \\ -1 & (-1-1)/(2) = -1 & (-1, -1) \\ 1 & (1-1)/(2) = 0 & (1, 0) \\ 3 & (3-1)/(2) = 1 & (3, 1) \\ 5 & (5-1)/(2) = 2 & (5, 2) \\ Step 3: Plot the graphs on your graph sheet. • Draw a horizontal x-axis and a vertical y-axis, making sure they cross at the origin (0,0). • Label your axes 'x' and 'y'. • Choose a suitable scale for both axes, for example, 1 cm (or one large square) representing 1 unit. Mark the numbers along the axes. • Plot the points from the first table for y = 2x + 1. Once plotted, use a ruler to draw a straight line through these points. Label this line as y = 2x + 1. • Plot the points from the second table for y = (x-1)/(2). Use a ruler to draw a straight line through these points. Label this line as y = (x-1)/(2). Step 4: Determine the equation of the line of symmetry. Observe the relationship between the two graphs. They are reflections of each other across a specific line. This line passes through points like (0,0), (1,1), (-1,-1), etc. This is the line y=x. The equation of the line of symmetry is y = x. That's 2 down. 3 left today — send the next one.