Question

what is the slope of the given line?

Explanation:

Step1: Identify two points on the line

We can see that the line passes through the origin \((0,0)\) and another point, for example, \((2, -2)\).

Step2: Use the slope formula

The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \((x_1, y_1)=(0,0)\) and \((x_2, y_2)=(2, -2)\) into the formula, we get:
\(m=\frac{-2 - 0}{2 - 0}=\frac{-2}{2}=-1\) (we can also simplify it as \(\frac{-1}{1}\) or just \(-1\), but since the problem asks for a fraction, we can write it as \(\frac{-1}{1}\) or \(\frac{-2}{2}\), but the simplest form is \(\frac{-1}{1}\) or just \(-1\). However, looking at the grid, another way is to take two points: from \((0,0)\) to \((2, -2)\), the rise is \(-2\) and run is \(2\), so slope is \(\frac{-2}{2}=-\frac{1}{1}\) or \(-1\). But if we take \((-2, 1)\) and \((2, -1)\) (wait, no, let's check the graph again. The line passes through (0,0), (2, -2), (-2, 2). So let's take (0,0) and (2, -2). Then slope is \(\frac{-2 - 0}{2 - 0}=\frac{-2}{2}=-\frac{1}{1}\) or \(-1\). Alternatively, using ( - 2, 2) and (2, - 2): slope is \(\frac{-2 - 2}{2 - (-2)}=\frac{-4}{4}=-1\). So the slope is \(-\frac{1}{1}\) or just \(-1\). But the problem has a fraction box, so we can write it as \(\frac{-1}{1}\) or \(\frac{-2}{2}\), but the simplest is \(\frac{-1}{1}\) or \(-1\). Wait, maybe the intended points are (0,0) and (2, -2), so slope is \(\frac{-2}{2}=-\frac{1}{1}\) or \(-1\). So the slope is \(-\frac{1}{1}\) (or \(-1\)).

Answer:

\(\boxed{-\dfrac{1}{1}}\) (or simply \(\boxed{-1}\), but since the problem has a fraction format, \(-\dfrac{1}{1}\) is appropriate)