To write the linear equation in the form \( y = mx + b \) using the points \((6, 16)\) and \((15, 43)\), we need to find the slope \( m \) and the y-intercept \( b \).
- Calculate the slope \( m \) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can set \((x_1, y_1) = (6, 16)\) and \((x_2, y_2) = (15, 43)\):
\[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
- Use the slope \( m \) and one of the points to solve for the y-intercept \( b \). We can use the point \((6, 16)\):
The equation of a line is \( y = mx + b \). Substituting \( m \) and the coordinates of the point:
\[ 16 = 3(6) + b \]
\[ 16 = 18 + b \]
\[ b = 16 - 18 = -2 \]
- Write the final equation:
Now we have:
- Slope \( m = 3 \)
- Y-intercept \( b = -2 \)
Thus, the equation of the linear function is:
\[ y = 3x - 2 \]