To find the equation of the linear function that models the relationship shown in the table, we'll first determine the slope (m) using the two points given: (6, 16) and (15, 43).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points (6, 16) and (15, 43):
- \(x_1 = 6, y_1 = 16\)
- \(x_2 = 15, y_2 = 43\)
Calculating the slope:
\[ m = \frac{43 - 16}{15 - 6} = \frac{27}{9} = 3 \]
Now that we have the slope \(m = 3\), we can use the point-slope form of the equation to find the y-intercept \(b\). We can use one of the points, let's use (6, 16):
The equation in slope-intercept form is:
\[ y = mx + b \]
Substituting for \(m\) and the point (6, 16):
\[ 16 = 3(6) + b \]
Calculating:
\[ 16 = 18 + b \]
Solving for \(b\):
\[ b = 16 - 18 = -2 \]
Now we have both the slope and the y-intercept. The equation of the linear function is:
\[ y = 3x - 2 \]
So, the equation in \(y = mx + b\) form is:
\[ \boxed{y = 3x - 2} \]