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=(1213)x−(11113)
y equals left parenthesis Start Fraction 12 over 13 End Fraction right parenthesis x minus Start Fraction 111 over 13 End Fraction right parenthesis

y=(−1312)x+(72)
y equals left parenthesis Start Fraction negative 13 over 12 End Fraction right parenthesis x plus Start Fraction 7 over 2 End Fraction right parenthesis

y=(1312)x−(192)
y equals left parenthesis Start Fraction 13 over 12 End Fraction right parenthesis x minus Start Fraction 19 over 2 End Fraction right parenthesis

y=−192
y equals Start Fraction negative 19 over 12 End Fraction
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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).

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

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

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

Using the points \( (18, 10) \) and \( (6, -3) \):

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

2. **Use the point-slope form of the equation**:

The point-slope form is:

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

We can use either point; let’s use \( (18, 10) \):

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

3. **Rearranging to slope-intercept form (y = mx + b)**:

Expanding the equation:

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

Calculating \( \frac{13}{12} \times 18 \):

\[
\frac{13 \times 18}{12} = \frac{234}{12} = 19.5
\]

So:

\[
y - 10 = \frac{13}{12}x - 19.5
\]

Now, add 10 to both sides:

\[
y = \frac{13}{12}x - 19.5 + 10
\]

Since 19.5 equals 19.5 and 10 combined gives \(-9.5\):

Converting -9.5 into a fraction gives \(-\frac{19}{2}\).

Thus:

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

4. **Matching with the provided responses**:

The correct equation is:

\[
y = \left(\frac{13}{12}\right)x - \left(\frac{19}{2}\right)
\]

Therefore, the answer is:

**y = (1312)x − (192)**