Find the equation of the line that passes through the points $(-5, -3)$ and $(10, -6)$.

1. Problem Description

Find the equation of the line that passes through the points $(-5, -3)$ and $(10, -6)$.

2. Solution Steps

First, we need to find the slope ($m$) of the line. The slope is given by the formula:

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

Using the given points $(-5, -3)$ and $(10, -6)$, let $(x_1, y_1) = (-5, -3)$ and $(x_2, y_2) = (10, -6)$.

$m = \frac{-6 - (-3)}{10 - (-5)} = \frac{-6 + 3}{10 + 5} = \frac{-3}{15} = -\frac{1}{5}$

Now that we have the slope, we can use the point-slope form of a line, which is:

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

We can use either of the given points. Let's use $(-5, -3)$.

$y - (-3) = -\frac{1}{5}(x - (-5))$

$y + 3 = -\frac{1}{5}(x + 5)$

$y + 3 = -\frac{1}{5}x - 1$

$y = -\frac{1}{5}x - 1 - 3$

$y = -\frac{1}{5}x - 4$

3. Final Answer

The equation of the line is $y = -\frac{1}{5}x - 4$.