To find the equation of the linear function in the form \( y = mx + b \) using the provided data points, we first identify the points from the table:
- The first point is \( (11, 58) \).
- The second point is \( (20, 103) \).
Next, we calculate the slope \( m \) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points:
- \( (x_1, y_1) = (11, 58) \)
- \( (x_2, y_2) = (20, 103) \)
We get:
\[ m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \]
Now that we have the slope \( m = 5 \), we can use one of the points to find the y-intercept \( b \). We can use the point \( (11, 58) \).
The equation can be written as:
\[ y = mx + b \implies 58 = 5(11) + b \]
Calculating:
\[ 58 = 55 + b \]
Solving for \( b \):
\[ b = 58 - 55 = 3 \]
Therefore, the equation of the linear function is:
\[ y = 5x + 3 \]
Thus, the final equation is:
\[ \boxed{y = 5x + 3} \]