How do you find the Y intercept of a table?

As an expert in mathematical analysis, I can guide you through the process of finding the Y-intercept from a table of data. The Y-intercept of a linear equation is the point where the line crosses the Y-axis. In the context of a table, it's the value of Y when X is equal to zero.

To find the Y-intercept from a table, follow these steps:

1. **Identify the column or row where X is zero**. If there is no entry for X = 0, you may need to estimate it by using the two closest points to X = 0 and finding the corresponding Y values.

2. Look at the corresponding Y value when X is zero. This is your Y-intercept.
3. If you need to estimate and cannot find an exact X = 0 in the table, use linear interpolation. This involves finding the equation of the line between the two closest points to X = 0 and then solving for Y when X = 0.

Here's an example to illustrate the process:

Suppose you have a table with the following data:
```
X | Y
---------------------
-1 | 1
0 | b
1 | 3
```

The Y-intercept is the value of Y when X is zero, which in this table is directly given as 'b'.

If the table did not have an entry for X = 0, you would use the two closest X values to estimate the Y-intercept. For example, if you had the following table:
```
X | Y
---------------------
-1 | 1
1 | 3
```

You would estimate the Y-intercept by drawing a line between the points (-1, 1) and (1, 3) and finding where it crosses the Y-axis (X = 0).

Next, to find the slope of the line, remember that the rate of change is equal to the slope. To find the y-intercept, substitute the slope in for m in the formula y = mx + b, and substitute a given ordered pair in the table for x and y in the formula, then solve for b.