Question

the graph of the linear function passes through the points (4, 24) and (6, 30).
what is the equation of the function

Answer 1

To find the equation of the linear function that passes through the points \( (4, 24) \) and \( (6, 30) \), we can follow these steps:

1. **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 \( (x_2, y_2) = (6, 30) \):

\[
m = \frac{30 - 24}{6 - 4} = \frac{6}{2} = 3
\]

2. **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 \( m = 3 \):

\[
y - 24 = 3(x - 4)
\]

3. **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:

\[
\boxed{y = 3x + 12}
\]