Question

Use the table to answer the question.
x y
18 10
6 -3
Write the equation of the linear function represented by the table.

Answer 1

To find the equation of the linear function represented by the table, we can use the two points provided: \( (18, 10) \) and \( (6, -3) \).

We can start by calculating the slope \( m \) of the line using the formula:

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

Assigning our points as follows:

- \( (x_1, y_1) = (18, 10) \)
- \( (x_2, y_2) = (6, -3) \)

We plug in the values:

\[
m = \frac{-3 - 10}{6 - 18} = \frac{-13}{-12} = \frac{13}{12}
\]

Now that we have the slope, we can use the point-slope form of the linear equation, which is given by:

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

We can use one of the points, say \( (18, 10) \):

\[
y - 10 = \frac{13}{12}(x - 18)
\]

Now, let's simplify the equation:

\[
y - 10 = \frac{13}{12}x - \frac{13}{12} \cdot 18
\]
\[
y - 10 = \frac{13}{12}x - \frac{234}{12}
\]
\[
y - 10 = \frac{13}{12}x - 19.5
\]
\[
y = \frac{13}{12}x - 19.5 + 10
\]
\[
y = \frac{13}{12}x - 9.5
\]

Thus, the equation of the linear function represented by the table is:

\[
y = \frac{13}{12}x - 9.5
\]