Line Through Points (-5,10) and (0,0): Coordinate Geometry Analysis

The problem asks us to find the slope of the line passing through the points $(-5, 10)$ and $(0, 0)$. To solve this, we'll follow these steps:

• Step 1: Note the coordinates of the two points. Let $(x_1, y_1) = (-5, 10)$ and $(x_2, y_2) = (0, 0)$.
• Step 2: Apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Substitute the values from the points into the formula and simplify.

Now, let's substitute and compute the slope:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 10}{0 - (-5)} = \frac{-10}{5}$.

Simplifying, we get $m = -2$.

Therefore, the slope of the line is $m = -2$.