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 \(b\) using the points given in the table.
The two points from the table are:
- Point 1: \((11, 58)\)
- Point 2: \((20, 103)\)
Step 1: Calculate the slope (m)
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \(x_1 = 11\), \(y_1 = 58\)
- \(x_2 = 20\), \(y_2 = 103\)
Calculating the slope:
\[ m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \]
Step 2: Use the slope to find the y-intercept (b)
We can use one of the points and the slope to solve for \(b\) in the equation \(y = mx + b\). We will use the first point \((11, 58)\):
\[ y = mx + b \] \[ 58 = 5(11) + b \] \[ 58 = 55 + b \] \[ b = 58 - 55 = 3 \]
Step 3: Write the equation
Now that we have \(m = 5\) and \(b = 3\), we can write the equation of the linear function:
\[ y = 5x + 3 \]
So the final answer is:
\[ \boxed{y = 5x + 3} \]