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

We can see that the line passes through the origin \((0, 0)\) and another point, for example, when \(x = 1\), \(y=-2\) (or we can use the point \((-4, 8)\) as seen from the graph). Let's use \((0, 0)\) and \((1, -2)\).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(1, -2)\). Then \(m=\frac{-2 - 0}{1 - 0}=\frac{-2}{1}=-2\). We can also verify with another point, say \((-4, 8)\) and \((0, 0)\). Then \(m=\frac{0 - 8}{0 - (-4)}=\frac{-8}{4}=-2\).

Answer:

\(-2\)