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 two points given in the table.
The two points are (6, 16) and (15, 43).
Step 1: Calculate the slope \( m \)
The formula for the slope \( m \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values from the points (6, 16) and (15, 43):
\[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
Step 2: Use the slope and one of the points to find \( b \)
We can use the slope-intercept form \( y = mx + b \) and substitute one of the points. We'll use the point (6, 16):
\[ 16 = 3(6) + b \]
Calculating \( 3(6) \):
\[ 16 = 18 + b \]
Now, solve for \( b \):
\[ b = 16 - 18 = -2 \]
Step 3: Write the equation
Now that we have \( m = 3 \) and \( b = -2 \), we can write the equation of the linear function:
\[ y = 3x - 2 \]
So the answer is:
\[ y = 3x - 2 \]