Question

find the rate of change. enter your response as an improper fraction.

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 \(x = 2\), \(y=-3\) (by counting the grid squares: moving 2 units to the right on the x - axis and 3 units down on the y - axis). So two points are \((0,0)\) and \((2, - 3)\).

Step2: Use the slope formula

The rate of change (slope \(m\)) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,-3)\) into the formula:
\(m=\frac{-3 - 0}{2 - 0}=\frac{-3}{2}\)

Answer:

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