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 will follow these steps:

1. **Calculate the slope (m)** using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, \((x_1, y_1) = (4, 24)\) and \((x_2, y_2) = (6, 30)\).

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

2. **Use the point-slope form of a linear equation**, which is:

\[
y - y_1 = m(x - x_1)
\]

We can use one of the points, say \((4, 24)\), and the slope \(m = 3\).

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

3. **Simplify this equation**:

\[
y - 24 = 3x - 12
\]

\[
y = 3x - 12 + 24
\]

\[
y = 3x + 12
\]

4. **Write the final equation** of the line:

\[
y = 3x + 12
\]

Thus, the equation of the linear function is \(y = 3x + 12\).