To determine the linear function that models the relationship shown in the table, we can start by identifying the values given:
| X | Y | |---|----| | 4 | 38 | | 6 | 58 |
Next, let's find the slope (m) of the line using the points (4, 38) and (6, 58). The formula for slope is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (4, 38) as \((x_1, y_1)\) and (6, 58) as \((x_2, y_2)\):
\[ m = \frac{58 - 38}{6 - 4} = \frac{20}{2} = 10 \]
Now that we have the slope \(m = 10\), we can use the point-slope form of the equation \(y - y_1 = m(x - x_1)\). Using the point (4, 38):
\[ y - 38 = 10(x - 4) \]
Expanding this:
\[ y - 38 = 10x - 40 \]
Adding 38 to both sides:
\[ y = 10x - 2 \]
Thus, the equation of the linear function that models the relationship shown in the table is:
\[ \boxed{y = 10x - 2} \]
This matches one of the options given.