To find the equation of the linear function in the form \( y = mx + b \), we first need to calculate the slope \( m \) using the two given points: \( (6, 16) \) and \( (15, 43) \).
- Calculate the slope \( m \) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \( (x_1, y_1) = (6, 16) \) and \( (x_2, y_2) = (15, 43) \).
Plugging in the values:
\[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
- Now we have the slope \( m = 3 \). Next, we use one of the points to find the y-intercept \( b \). We'll use the point \( (6, 16) \).
Using the equation \( y = mx + b \):
\[ 16 = 3(6) + b \]
Simplifying:
\[ 16 = 18 + b \]
\[ b = 16 - 18 = -2 \]
- Now we have both \( m \) and \( b \). The equation of the linear function is:
\[ y = 3x - 2 \]
Thus, the final answer is:
\[ \boxed{y = 3x - 2} \]