To solve this problem, we need to find the linear function that fits the points given in the table.

The table provides the following points:

$(-4, 10),\ (-2, 7),\ (6, -5)$

Step 1: Calculate the slope of the line (m).

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's use the points $(-4, 10)$ and $(-2, 7)$ first:

$m = \frac{7 - 10}{-2 - (-4)} = \frac{-3}{-2 + 4} = \frac{-3}{2}$

The slope $m$ is $-\frac{3}{2}$.

Step 2: Check the slope with other points.

Now, let's check the slope using the points $(-2, 7)$ and $(6, -5)$:

$m = \frac{-5 - 7}{6 - (-2)} = \frac{-12}{6 + 2} = \frac{-12}{8} = \frac{-3}{2}$

The slope is consistent, so the slope of the line is indeed $m = -\frac{3}{2}$.

Step 3: Use the point-slope form to find the equation.

We can use the point-slope form of the equation:

$y - y_1 = m(x - x_1)$

Using the point $(-4, 10)$ and the slope $m = -\frac{3}{2}$, we plug in the values:

$y - 10 = -\frac{3}{2}(x - (-4)) = -\frac{3}{2}(x + 4)$

Distribute the $-\frac{3}{2}$:

$y - 10 = -\frac{3}{2}x - 6$

Now solve for $y$:

$y = -\frac{3}{2}x + 4$

Step 4: Check the answer.

The correct equation is:

$y = -\frac{3}{2}x + 4$

So the correct