The graph in the image shows a piecewise linear function. Let's break it down into two parts based on the different line segments.

1. First Line Segment: This segment is a straight line from the point $(-10, 6)$ to $(-2, 0)$. To find the equation of this line, we need to determine its slope and intercept:

   • Slope ($m$) = $\frac{0 - 6}{-2 + 10} = \frac{-6}{8} = -\frac{3}{4}$
   • Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, with the point $(-2, 0)$, the equation becomes: $y - 0 = -\frac{3}{4}(x + 2) \quad \Rightarrow \quad y = -\frac{3}{4}x - \frac{3}{2}$ This line is valid for $x$ values between $-10 \leq x \leq -2$.

2. Second Line Segment: The second segment goes from the point $(-2, 0)$ to $(10, -8)$. Let's calculate the slope for this segment:

   • Slope ($m$) = $\frac{-8 - 0}{10 + 2} = \frac{-8}{12} = -\frac{2}{3}$
   • Using the point-slope form with the point $(-2, 0)$, the equation becomes: $y - 0 = -\frac{2}{3}(x + 2) \quad \Rightarrow \quad y = -\frac{2}{3}x - \frac{4}{3}$ This line is valid for $x$ values between $-2 < x \leq 10$.

The complete piecewise function is: