The problem asks us to find the equation of a line that has a slope of $-\frac{4}{5}$ and passes through the point $(-10, 6)$.

1. Problem Description

The problem asks us to find the equation of a line that has a slope of $-\frac{4}{5}$ and passes through the point $(-10, 6)$.

2. Solution Steps

We can use the point-slope form of a linear equation, which is:

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

where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

In this problem, we have $m = -\frac{4}{5}$ and $(x_1, y_1) = (-10, 6)$.

Plugging these values into the point-slope form, we get:

$y - 6 = -\frac{4}{5}(x - (-10))$

$y - 6 = -\frac{4}{5}(x + 10)$

Now, let's simplify the equation and convert it to slope-intercept form, $y = mx + b$.

$y - 6 = -\frac{4}{5}x - \frac{4}{5}(10)$

$y - 6 = -\frac{4}{5}x - 8$

$y = -\frac{4}{5}x - 8 + 6$

$y = -\frac{4}{5}x - 2$

3. Final Answer

The equation of the line is $y = -\frac{4}{5}x - 2$.