Question

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

Answer 1

To include a y-intercept in a table, you need to identify the point where the input (x-value) is zero. The y-intercept is the point where the graph of a function crosses the y-axis, and this occurs when x = 0.

If you have a table of input-output pairs but do not yet have a row where x = 0, you can extend the pattern by finding the output (y-value) when the input is zero.

For example, if your current table looks like this:

| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

You might notice that the output seems to be following the pattern \( y = 2x \). To find the y-intercept, substitute \( x = 0 \) into the equation:

\[
y = 2(0) = 0
\]

Now you can add this input-output pair to the table:

| x | y |
|---|---|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

Now the table includes the y-intercept (0, 0). If you provide the specific function or data you have, I can help determine the y-intercept more accurately.