The graph of a linear function is shown on the grid.

To find the equation of the linear function represented by the points \((-4, 3)\) and \((4, 11)\), we can use the slope-intercept form of a linear equation, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. **Calculate the slope (m)**:
The slope can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-4, 3)\) (let's call this \((x_1, y_1)\)) and \((4, 11)\) (let's call this \((x_2, y_2)\)):
\[
m = \frac{11 - 3}{4 - (-4)} = \frac{8}{4 + 4} = \frac{8}{8} = 1
\]

2. **Find the y-intercept (b)**:
We can use one of the points to solve for \(b\). Using the point \((4, 11)\):
\[
y = mx + b
\]
Substituting the values:
\[
11 = 1(4) + b \\
11 = 4 + b \\
b = 11 - 4 \\
b = 7
\]

3. **Write the equation**:
Now that we have \(m = 1\) and \(b = 7\), we can write the equation of the line:
\[
y = 1x + 7 \\
y = x + 7
\]

Thus, the equation best represented by the graph given the points is:
\[
y = x + 7
\]