How do you determine the slope of the function from the given table of values?

To find the slope of a function represented by a table of values, you can follow these steps:

1. Identify the coordinates: Each row in the table represents a point on the Cartesian plane, typically in the form of (x, y). For example, if your table shows:
• (1, 2)
• (2, 3)
• (3, 5)
2. Use the slope formula: The slope (m) between any two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
• m = (y₂ – y₁) / (x₂ – x₁)
3. Select two points: Choose any two points from the table to apply the formula. Using the previous example, you could select (1, 2) and (2, 3).
4. Plug in the values: Using the points (1, 2) and (2, 3):
• m = (3 – 2) / (2 – 1)
• m = 1 / 1 = 1
5. Repeat for consistency: To ensure the slope is consistent across the table, you can calculate the slope using another pair of points. For instance, using (2, 3) and (3, 5):
• m = (5 – 3) / (3 – 2)
• m = 2 / 1 = 2

In this case, you would notice a change in slope. You can conclude that the function may not be linear, and the slope varies depending on the points selected. If the slopes calculated are consistent, you can confirm that the function is linear, and the slope is constant.

Additional Notes: If you find the slope is different depending on the points you choose, the function might be non-linear, so you may consider looking at the nature of the function or plotting the points for a visual representation.