To determine the equation of the linear function represented by the given points, we first find the slope \( m \) using the two points from the table: \( (18, 10) \) and \( (6, -3) \).
The formula for the slope \( m \) between the points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the coordinates:
\[ m = \frac{-3 - 10}{6 - 18} = \frac{-13}{-12} = \frac{13}{12} \]
Now that we have the slope, we can use the point-slope form of the linear equation to find the y-intercept. We will use one of the points; let’s use \( (18, 10) \).
The point-slope form of a linear equation is:
\[ y - y_1 = m(x - x_1) \]
Plugging in the slope \( m = \frac{13}{12} \) and the point \( (18, 10) \):
\[ y - 10 = \frac{13}{12}(x - 18) \]
Now, we simplify this equation:
\[ y - 10 = \frac{13}{12}x - \frac{13}{12} \cdot 18 \]
Calculating \( \frac{13}{12} \cdot 18 \):
\[ \frac{13 \cdot 18}{12} = \frac{234}{12} = \frac{39}{2} \]
Therefore:
\[ y - 10 = \frac{13}{12}x - \frac{39}{2} \]
Now, add 10 to both sides to isolate \( y \):
\[ y = \frac{13}{12}x - \frac{39}{2} + 10 \]
Converting 10 to a fraction with a common denominator of 2 gives us:
\[ 10 = \frac{20}{2} \]
Thus, we have:
\[ y = \frac{13}{12}x - \frac{39}{2} + \frac{20}{2} \]
This simplifies to:
\[ y = \frac{13}{12}x - \frac{19}{2} \]
Therefore, the equation of the linear function is:
\[ y = \frac{13}{12}x - \frac{19}{2} \]
The correct response is:
y=(13/12)x−(19/2).