To find the equation of the linear function represented by the points (18, 10) and (6, -3), we can use the slope-intercept form of a linear equation:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
First, we calculate the slope \( m \) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (18, 10) and (6, -3):
- Let \( (x_1, y_1) = (18, 10) \)
- Let \( (x_2, y_2) = (6, -3) \)
Now substitute:
\[ m = \frac{-3 - 10}{6 - 18} = \frac{-13}{-12} = \frac{13}{12} \]
Now that we have the slope \( m = \frac{13}{12} \), we can use one of the points to find the y-intercept \( b \). We'll use the point (18, 10):
\[ y = mx + b \] \[ 10 = \frac{13}{12}(18) + b \]
Calculating \( \frac{13}{12} \cdot 18 \):
\[ \frac{13 \cdot 18}{12} = \frac{234}{12} = 19.5 \]
Now substitute this back into the equation:
\[ 10 = 19.5 + b \] \[ b = 10 - 19.5 = -9.5 \]
To express -9.5 in fractions:
\[ -9.5 = -\frac{19}{2} \]
Now substitute \( m \) and \( b \) back into the equation:
\[ y = \frac{13}{12}x - \frac{19}{2} \]
Therefore, the equation that represents the linear function from the table is:
\[ y = \frac{13}{12}x - \frac{19}{2} \]
So, the correct response is:
y=(13/12)x−(-19/2)