To find the equation of the linear function that passes through the points \( (4, 24) \) and \( (6, 30) \), we can follow these steps:
- Find the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we can assign \( (x_1, y_1) = (4, 24) \) and \( (x_2, y_2) = (6, 30) \):
\[ m = \frac{30 - 24}{6 - 4} = \frac{6}{2} = 3 \]
- Use the point-slope form of the equation of a line:
The point-slope form is given as:
\[ y - y_1 = m(x - x_1) \]
Using point \( (4, 24) \) and the slope \( m = 3 \):
\[ y - 24 = 3(x - 4) \]
- Simplify to get the slope-intercept form (y = mx + b):
Distributing the 3:
\[ y - 24 = 3x - 12 \]
Adding 24 to both sides:
\[ y = 3x + 12 \]
Thus, the equation of the linear function is:
\[ \boxed{y = 3x + 12} \]