To find the linear equation that fits the given points, we can first determine the slope (\(m\)) and y-intercept (\(b\)) of the line.
We can use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's take two points from the table, for instance, (21, 13) and (33, 25).
Using these points:
\[ m = \frac{25 - 13}{33 - 21} = \frac{12}{12} = 1 \]
Now we have a slope \(m = 1\). Next, we can use one of the points to find the y-intercept (\(b\)). We'll use the point (21, 13).
The equation of a line can be expressed as:
\[ y = mx + b \]
Substitute \(m = 1\) and the point (21, 13):
\[ 13 = 1(21) + b \]
This simplifies to:
\[ 13 = 21 + b \] \[ b = 13 - 21 \] \[ b = -8 \]
Now we can write the equation of the line:
\[ y = 1x - 8 \]
This can be simplified to:
\[ y = x - 8 \]
Thus, the equation that gives the rule for the table is:
\[ y = x - 8 \]