To create a table of ordered pairs for the equation \(y = -13x + 4\), we can select a few values for \(x\) and calculate the corresponding \(y\) values.
Here’s how it looks:
| \(x\) | \(y = -13x + 4\) | |-------|-------------------| | -2 | \(y = -13(-2) + 4 = 26 + 4 = 30\) | | -1 | \(y = -13(-1) + 4 = 13 + 4 = 17\) | | 0 | \(y = -13(0) + 4 = 0 + 4 = 4\) | | 1 | \(y = -13(1) + 4 = -13 + 4 = -9\) | | 2 | \(y = -13(2) + 4 = -26 + 4 = -22\) |
Now we have the following ordered pairs:
- For \(x = -2\), \(y = 30\) → (-2, 30)
- For \(x = -1\), \(y = 17\) → (-1, 17)
- For \(x = 0\), \(y = 4\) → (0, 4)
- For \(x = 1\), \(y = -9\) → (1, -9)
- For \(x = 2\), \(y = -22\) → (2, -22)
Selected Points for Graphing
Let's select two points for plotting:
- \((-1, 17)\)
- \( (0, 4) \)
Plotting the Points
- Point (-1, 17): Move 1 unit to the left on the x-axis and 17 units up on the y-axis.
- Point (0, 4): This point is at the origin where x is 0 and y is 4.
Graph Plotting
When you graph these points, ensure that the horizontal axis goes from -10.8 to 10.8 and the vertical axis goes from -10.8 to 10.8, appropriately marking the scale. After plotting these two points, you can draw a line through them to represent the equation \(y = -13x + 4\).
Graph Line
Since this is a linear equation, you can further extend the line in both directions to complete the graph. The slope indicates that for every 1 unit increase in \(x\), \(y\) decreases by 13 units. Therefore, the line will be steeply downward sloping due to the negative slope of -13.
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