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