Question

1. graph of a line on a coordinate grid with x and y axes labeled, grid lines, and the line passing through the origin and other points 3)

Explanation:

Step1: Identify two points on the line

We can see that the line passes through \((0, 0)\) and \((1, -1)\) (or other points like \((-1, 1)\), \((2, -2)\) etc.). Let's use \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(1, -1)\).

Step2: Calculate the slope \(m\)

The formula for slope is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values, we get \(m=\frac{-1 - 0}{1 - 0}=-1\).

Step3: Determine the equation of the line

Using the slope - intercept form \(y = mx + b\), and since the line passes through \((0, 0)\), the \(y\) - intercept \(b = 0\). So the equation of the line is \(y=-x\) or \(y=-1x + 0\).

Answer:

The equation of the line is \(y=-x\) (or \(y=-1x\))