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: Prepare the table of values for y = 2x + 5. To draw the graph, first calculate the y values for x ranging from -3 to 4. | x | 2x | +5 | y = 2x + 5 | (x, y) | |:---:|:----:|:----:|:------------:|:--------:| | -3 | -6 | +5 | -1 | (-3, -1) | | -2 | -4 | +5 | 1 | (-2, 1) | | -1 | -2 | +5 | 3 | (-1, 3) | | 0 | 0 | +5 | 5 | (0, 5) | | 1 | 2 | +5 | 7 | (1, 7) | | 2 | 4 | +5 | 9 | (2, 9) | | 3 | 6 | +5 | 11 | (3, 11) | | 4 | 8 | +5 | 13 | (4, 13) | Step 2: Plot the graph using the given scale. • Draw a horizontal x-axis and a vertical y-axis on graph paper. • Mark the origin (0,0) where the axes intersect. • Apply the scale: 2 cm represents 1 unit on both axes. This means that every 2 cm grid line (or every large square) should be labeled as 1, 2, 3, for positive values and -1, -2, -3, for negative values on both axes. • Plot each point from the table above on your graph paper. For example, for (-3, -1), move 3 units left on the x-axis and 1 unit down on the y-axis. • Once all points are plotted, use a ruler to draw a straight line that passes through all these points. Extend the line to the edges of your graph paper. • Label the line with its equation: y = 2x + 5. This process will create the graph of the linear equation. What's next?