Question

what is the slope of this line? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and another point, for example, \((1, -2)\) (we can also use other points like \((2, -4)\), etc.).

Step2: Use the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0,0)\) as \((x_1, y_1)\) and \((1, -2)\) as \((x_2, y_2)\), we substitute into the formula: \(m=\frac{-2 - 0}{1 - 0}=\frac{-2}{1}=-2\). We can also check with another point, say \((2, -4)\): \(m=\frac{-4 - 0}{2 - 0}=\frac{-4}{2}=-2\), which confirms the slope.

Answer:

\(-2\)