To find the equation of the linear function in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).
- First, calculate the slope \( m \) using the two points provided in the table: \( (11, 58) \) and \( (20, 103) \).
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points \( (11, 58) \) and \( (20, 103) \):
\[ m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \]
- Now we have the slope \( m = 5 \). To find the y-intercept \( b \), we can use one of the points. Let's use the point \( (11, 58) \).
Using the equation \( y = mx + b \):
\[ 58 = 5(11) + b \] \[ 58 = 55 + b \] \[ b = 58 - 55 = 3 \]
- Now, we can write the equation of the linear function:
\[ y = 5x + 3 \]
Thus, the equation of the linear function that models the relationship shown in the table is \( \boxed{y = 5x + 3} \).
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