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.

(1 point)
Responses

y=(12/13)x−(111/13)

y=(13/12)x−(-19/2)

y=−19/2

y=(−13/12)x+(7/2)

Answer 1

To determine the equation of the linear function represented by the points in the table, we first need to calculate the slope (m) using the two given points: (18, 10) and (6, -3).

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Assign values from the points:
- \((x_1, y_1) = (18, 10)\)
- \((x_2, y_2) = (6, -3)\)

Now plug these values into the slope formula:

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

Now that we have the slope \(m = \frac{13}{12}\), we can use the point-slope form of the equation of a line:

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

Using the point \((18, 10)\):

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

Now distribute \( \frac{13}{12} \):

\[
y - 10 = \frac{13}{12}x - \frac{13}{12} \times 18
\]
\[
y - 10 = \frac{13}{12}x - \frac{234}{12}
\]
\[
y - 10 = \frac{13}{12}x - \frac{39}{2}
\]

Now, add 10 to both sides:

\[
y = \frac{13}{12}x - \frac{39}{2} + 10
\]

Convert 10 to a fraction with a denominator of 2:

\[
10 = \frac{20}{2}
\]

So:

\[
y = \frac{13}{12}x - \frac{39}{2} + \frac{20}{2}
\]
\[
y = \frac{13}{12}x - \frac{19}{2}
\]

Thus, the equation of the linear function is:

\[
y = \frac{13}{12}x - \frac{19}{2}
\]

This matches with the option:

**y = (13/12)x - (-19/2)**

Hence, the correct response is:

**y = (13/12)x - (-19/2)**