Question

explanation
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, \((3, -2)\) (we can also use other points like \((6, -4)\) etc.).

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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(0,0)\) and \((x_2, y_2)=(3, -2)\). Then \(m = \frac{-2 - 0}{3 - 0}=\frac{-2}{3}\). We can also check with another point, say \((6, -4)\), then \(m=\frac{-4 - 0}{6 - 0}=\frac{-4}{6}=-\frac{2}{3}\) (after simplifying the fraction by dividing numerator and denominator by 2).

Answer:

\(-\frac{2}{3}\)