Question

.

If the y-intercept is not in a table, extend the pattern so that the table now includes an input-output pair where *blank*

A x = y
B x = 0
C (0, 0)
D y = 0

Answer 1

To extend the pattern and include an input-output pair where the y-intercept is present, we need to consider what the y-intercept represents in a function or table of values:

1. The y-intercept occurs when \( x = 0 \).
2. At this point, the corresponding \( y \) value should be noted, typically as a coordinate (0, y).

Let’s examine the options given:

- **A** \( x = y \) - This suggests a relationship but does not indicate a specific point to find the y-intercept.
- **B** \( x = 0 \) - This indicates the x value for the y-intercept but does not provide y.
- **C** (0, 0) - This explicitly states the y-intercept is at (0, 0), which is a valid point.
- **D** \( y = 0 \) - This means that for some specific x values, y equals 0, which may indicate a horizontal line at y = 0.

The best choice to complete the table with an input-output pair representing the y-intercept is **C (0, 0)**, assuming the y-intercept of the function or relation we are analyzing is indeed (0, 0). This means that when \( x \) is 0, \( y \) is also 0, thereby reinforcing that the line crosses the y-axis at this point.

To illustrate clearly, if you have a table of values that lists different x numbers and their corresponding y values, you can include (0, 0) to indicate where the graph intersects the y-axis.

So the extended pattern in your table could look something like this:

| x | y |
|---|---|
|...|...|
| 0 | 0 | (This is the y-intercept) |
|...|...|

If you have further details that specify what the function is, please share for a more tailored response!