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 (\( b \)).
- Calculate the slope (\( m \)): The slope formula is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (6, 16) \) and \( (15, 43) \):
- \( x_1 = 6 \), \( y_1 = 16 \)
- \( x_2 = 15 \), \( y_2 = 43 \)
Substituting the values into the slope formula:
\[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
- Use one of the points to find the y-intercept (\( b \)): We can use the point \( (6, 16) \) and the slope \( m = 3 \) in the equation \( y = mx + b \):
\[ 16 = 3(6) + b \]
This simplifies to:
\[ 16 = 18 + b \]
Now, solve for \( b \):
\[ b = 16 - 18 = -2 \]
- Write the final equation: Now that we have \( m \) and \( b \), we can write the equation:
\[ y = 3x - 2 \]
Thus, the equation of the linear function is:
\[ y = 3x - 2 \]